(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 7.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 153680, 3251] NotebookOptionsPosition[ 125975, 2656] NotebookOutlinePosition[ 152839, 3230] CellTagsIndexPosition[ 152726, 3224] WindowTitle->Probability Densities, Expectation Values, and Uncertainties for \ Gaussian Wavepackets WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[ GraphicsBox[RasterBox[CompressedData[" 1:eJztvXlwHOl1J6iIjdg/17PjWWsVli3J47Fle2JiY+yZkQjUkVmFiwTBs3mB gLtbh8dud7fGjpjxaDQzG16rLWt8qKXWQRD3VagD4H3jrAKqUCfOAkDiItkk CPAAiYNkk0RV7TsyE1mFKlwE2GArO75GfPXLl+9735FZ9f343vu+8vb7e9/+ 3z73uc/9Jvxv/N8/9zmsi8cHoZhLrkLZjLqpeMB0/BoUxIuuYqV4GK4aigeF 44Om4iGSD0NFvhQW6F74KBYPgWTGcbwEoHBsCLSJJQOS/qJB1Fw8JBQN8O1Q ARm4SyABoTgMINwuUB0qdGMY/4IlxUPGoiFuK6OI7mU9YNKxq6BcJPNQIZuH 8gNQ4F6QR/0kz0Zy11B50VVWjh+5QnWULLpqLh4RqY/wMbNseGdx/77j/pzS MHcW2sXOlqAMazPhANIQsRIUw2KSxlYaNDPJSx9LR1g48/gIIiXDJDMiyZQM Zx5flMdKyQhrVuwUSqk5nrviAUk/dRP0gAYcGbCkhC4VDSqt8AgjWCINEV1S zS9PKw8LrQexpB8nrnSYh477xfMllA5mFl+FCuPQnMpm1JlxfECkwaF2w7h4 aJAle0qGcQEUD6ElJQPC8avSuuIpK77GdmJDjJcOsp3yuuX5GuZx4H5J9xZJ 44MV6GPpIDTByw+FaXxwbZMNkgzjOIZhGH+WYVykFaKM29y9b8ZmC1rCPzSX 8RK6ZizBcZPGmRdDkbQqsAlc7Vel54sGXFEo2z/Ma55X0WY/71pdq2t1ra7V tfrrWj82Yiq6AQUqwrGr4rEx8Rc3toptWl2rb2bdVNwvFveYcI8A+4huqJul zUgf1UdeEjeV9MIl3pIAuCgPdRkXjncn4LKeRPm14tAvKIzL+6ke3jvQ3pNs LhmU7j0+yPsmFT68JfGwvHdW2Q913KYt6de68CXtjghF/byf5T07jmEJbjfW ivPeStn7w/Izl8hb6WQ4b20UGkHaB6H8Gta5KcU+6HXBX8l7YGiDcGnvjGvm F8PCL0bpi/U6fLfi9yy/Z4gzWV9/lVt4MSgfNwqnEpZWKZM5VDKOD8GWHGki 2uCbi8LMMxCnMcD0EZTMYmWDH+a/Eg1VtLhomb5AWun4EFEuQ0pFYoSKJepD YlGKBpH6KJL4GRV1IxupPCYkwHSBUDQAFiqkGd8uPUFkvKrpIWUElNtBRiCu A9mG4n6oZxT1vVl39jtlNQXWS2APCEhkC73Gidwb4ObkrsUV9Xgi6VcclpZQ EZstCYBmanGIR4nkB+TZwbu4RbiKApLYoDS2xdd49JAmKpL4RpkGlGYclIPl i3NdLE0Kc1A8vyyJJCFNtGKbQhJKppIAdoFn7bj0gmLKTu7aEN8oT4G0JNCM Y1eXjgyyakXXlF4rV7mPAi0eHh++HReS3AVxcQyHVAKDtH7iWuGRkdYtrWcm XRcblQeBBxZJOdkMtSrAywMfdl//y9hs/s/cP4N1AqCRCdsSXH6gR1A/bkWL XY577mjB8JLgv2C8MoCb+rxruIZruIZruIa/jrj8Y1XaPS3+094Ws1PDNXzT 1v8QPwII8j+/Lu4awso/Rq8Pp78Dckn4uT6wKC9Lyn8T8KG14myMul1VGZAv DakkXydc6Zc8CGF5ZhP6O7BWXF4Y4aXy6rWUsJxWjyfMhVpyyTTFaUtYvakU Ll3n6qWy9fFUZan8ZuMvY3/8ipJZF4WTeYliCwibWux+0Q5/oe43QrH6DFav sa4T/0Ld5hOsfiqIi3U+Q12nUEcyANb5jCAAfy1eQ61bV+vGvxaPESudxjqf aPHq4RLcUtupr3ELdFUPl+ivvsaDt0AdK51G6S+KIQh30e1cMdR4oOiq3Xqq KAU06Go6EKx2p7MBoASUkw061sm21XjSQYyVgwDohF5gl/3SODiCInTHHjA4 APEJjlBmg3PP6YbtJzt31wVFELCEdDYeq4AojZ4yjPA3aIB75atKEeyLYiKP Nt8itavgflGSIWOkJkCnX7QG9HZFUmoC7VTa5UqdVDEoiA1BlaRsuVQP6mSd OPuKWkfQiJWgqFZOvRMUk+yLqgzqniqjYacOghK+kcwgbXLBS3LflaFzBJMN rLxQseLXq3H1X1zAsp1Lb4+7pKrY5L/Y6yD3RRpJLmCSlTSzvMNvaAlnxmYL wyN5kvEwdNwFmsS6xWUgqJozKDbIzUnTagnobdJwGeOs1YpWtKIVrWhFK4lF XFI+dZO0opVXUJaufFz8tJvYAJyb4F+8KpAr5viPQvzfjcFpX5DQbtJnPPk4 bG38la8Webux+HHNuBiPiynkl+AJZrz6vmtlI8s613Cdz4g0Ed27OXVDnQ/e VyZ4oRGJZLB4kQuqRKZIZ/HCi86EdBCSQliqOtLgEuBQqlneg38rXcbyNn1V u6GqQ1fZnl7drmPWCBEXfAQBfaVTV+HUVbqN1R1GrLvSqpzGKpe+vF0Pt9R0 IF5BMlXtQo1bgI/VbmrabQD58rZ0aKXCaaho1Ve0pcO99JH0uLDpMpcOWgE9 ULg5bJ2bdumrO8SaDj3e7kQjQTl3lt7VOCa1PpEfNBiQWr/BEcg479x/oSq3 oXW/I5SJPJLXaPGbHEHR4Rfs/kzVV4Agv/CxsqROMj7BGtDzR0sAcVToN8p1 M/GERuR5CLcSnYiGBfmjTIb4BEIE/pZhhXw7TCV8xcBV6AvMGmhGGZ/UQUCI bJTYJ2QgvRJ3h4QksZRIv/hEWg8C6YFx0Fm9oiXI60T6UqO6gU21ePVIeIJA kNeqge8F3CZ/CUpcKH39sXIeExhkpBB9Jr63lseKjCRq1AR2ggHUL9TPbcnz hfdCx7GOMkbUL9/LTbA9aIPPhOxrp4HsFBfbCpjReB/aj3W/kccHh9GH40Pj xjoNrLPGb2wOZ0VnC3vHcmt8BugCs3PMhcrjY2Qb6khPrTRHIrelsk36SWCV xlaybZOfd62u1bW6VtfqWv01rUu7IfjxBgXrQcOWsU2ra/VNrPMujLcYXJef BUGpo4eAV9qArBXnf/3n37G876N2Wb+E03Mn2IMm3ivxM2gPSjjLrxWnHaX6 uZY2OAoOzcnPe5x8Kj1bDedxk+eRvT70Sn/XjVNbelvc+1CMr4svX+f1xvsg FS+hxo28fuS6WV63rMe8mrUttyW8pvjrW1f6ouzNJfekgMIPGGVOQ1DLrFjf fPt5v4+lxkNsT3s6/EWiyYVOSuTFhIwWlKoOXUUrUklMK8FHJILadYCUtepL WvUO36GLve+f734XPoKS6nZDeZu+rBWpp4q29JLm9NKW9Mo2JJTKW3SlTenl rWkVrSgA8sxogQAUaB3UIhVGxFRVG+FNaedD37G53yhpTCtuSrN05Di8+0he B8orWlAGVFU79WQPFmwL9evL2wzEjBmOkxjgNR1oP7yTiRrCB7PWZ1beOfCx IZRxtvNga0nO6YuHTgd22vx6npd6f1Z9MNvWnmN1ZzoCGXiLD6khiash3kny p/ItTjfxVIIyuZaAcLIro20wuzmcc647o0723mFCieSROWT3njrJBUhZV5J7 D6ryisS9CM3hzJaBbNCJt5MfHfv81PqRPyG/IHoHyn5ctAaQyHIN5DQNZJ3p NtvoEskb2PnKERSb+zIb+7PtEqenvEtx2aCXWsBcHzS39Odc6ctyIJdlYJ7N htwU6oHKuR7oY9aZrkxbgPkxsscn1fkZaQ1nt/RnNeAXIvaxhtYkO6Gxneyb VIvtGiXnLuLE2gZyoIDxtew9GBJp7oxsPL/nma/jOtmMfYSP7OtVi69cbkuA drELIZHtr/HpYUih1IdMxGXRmHuNTQOZsdn8ntEdYFiVT8d6YEAu92bDhEJf SKeoPPtSHwd3wDjI/7oktxsQ2gYAz2QZh38LvdO0ulbX6lpdq2v1rVQXqa7s 40TCX8G/82p1rf7p19WclbqOoSWqOhTecq4VX6pfwYmzEqHEy+iZ+1py7/px 9o5Q1RP4ajEV3/U64KnsR5y4rw3A5T2sMak968Jx7cnzkmC/Glc4urj3sz2o 5u62xHP0+tcXOaV4XnHNuJqHVPNU6nZT4Uo9FW6Xo5A2qcisi1DXaah1C9Xt aZVtBrvnQCwWOxt6qwrfcnr0sOowVjmNFW3b2ge//2zhMdSRwmo3EtOFDlGn A29NPgzForGHj4ehPH/xuHu8FGkrp6G8RXdvbjgWicboP7i9Y+gD59AH/Jn+ RuY/uXsm+Gb39bKYJIUXnkfmazrQdQr01zpz7s+PgCRcCY2VVbfmXL1zFurX Ji84PAdu3G8HefnWiH/kp6eDb0ejUUl/NPZkYRb6BSZJTUZBUXT03nny5zHJ 0XBmh1+sD5j4Xxbqg9lnvEecxTkXTx0+FdxbF8qww1V/VkMw92TTnpPnt0Od R0+OrRPbBrOjcwWxWSj5zx4enpzc3zOedyYkcPjhYiifX+wdy43O5YMYlpmj 8w8OnO/Ohku913fB7aCHna9AbWy2cHJyLy8e+Ng7lgdI20AO8VrIegWv5T59 dBjuisweBW0D43n2kLR4WgayoJX+0Tyk18jI1oEsuL1nPBeuBoa3R2cLYzNH 4F4we2rq4ImQqAS+tYazQS0ZWQB16Agoh9uVLsNfMiafbs+Hzp7rzYzNFABo l2X6R3eDZi7cOlRIwEDuYUJwZOezh0doxFBJ//XdSgydayCbhW2SPzN2B8TI eCEwnEdDLbV+d/LgyS6T8sgoFRh50AMjjHfhcJmVYEZ2gYORlFsR7KrZhFF9 Pn0EbsQymx++sUsxDMdwpqBnbDeSjRhRKDSGMx/ePcJTz3+hOSk2M2gC5ZIq ugpTz3rA4PkHB2HWwH42wLbJD7tWtKIVrWhFK69psS0pSnS/VrTy2S+U54T/ sZsRynnCPzWZyxWVnaZt7TjpN8r6DSr9SjSZFKUi60nEFYUbgqcahMRKKoEt gscXxdtBPf6qsgl43FC/LM4bH9WlBHnV2kj2UV0+/Qfq5Uqqfr3u5TXqL3kf oUdKTYe+yimUNum9wx/GYpHBmzbON4Xhe+3p5S360hbd5HQvXGrq/x66NjmR 7AL8pPetZwuPY9FY++D3kc5ypUEFPo5OXChrNsBdZc26K71/xVRVjSunDB2x dNXObKabmsL/pcJpLHduK2/R1biymIS63PeOFFTYrgN8+M45kPzkxaxn6KM7 04Fnz+eJy4qM329rH/wA9J8Pvcc31rlzkTdr1dNdFwC5MxNC5y5AWtOgUTbD Ofg9UI5xbXIInt2bYXdlnfDmNgQybV3mE8EdTZ1v9x83u6v2XujOR7erUM5p /77TzUebyrJOXd5T3xXHX9kldqhgbvrAnalDE1N7mZmZe3D4Un+GLSBnuPIJ PWO7Y3OFtyf3dV7NbR3ICF7Lm5zcf6ILf4YRTVToDCOXxfFoyCzd2a9MVv8o UkZIcAXwpeHs3w4fp6cOu6/mugZyPr69j8gT5HzqggLogdsXuRTytgIBZEvA jPHcsVu7QUPrUOYNuHGmYOTWnrogfX8FDDdu7wWke3x3ezj7XG9m71huZK4A brdTeiiQaerbDsof3j3UMbTDNZD98e39xHdh60QAYnPPHx6E7rRf2+EZ2oHj M5gTmznSPZ7HqbHQmJkjD+4fcF9FN6qbE3tiM4XdYzuY62sb2BGdOwym1slJ sVrD2ZLxARxDMB4GHJpGU2fB+H3yKMW9yXlSekd3g04pzVcQeWY7/Qwg/ipf 5tyk4E2ivAof3DvkHcqBMYSuIWFFvBkowauzhWAAzZH+dCgDJvrZg8M91/eA hW2DmYNju3EQaLqJ4iu4f/cw9XEHTF9wZCf/PKBLh2/fOgBNXA5n46j6l34H aUUrWtGKVrSiFa1oRSu0kaRfsArJo1yS6Fy/ksNqEedfvAmqUuG2uE2rdFWd v9eWbD+baoe7Sjxhj2zfcDyF/SnxVdfXwXss5QRWaislT6XKn6zWs2G4ut3V 2LNGXFCD8WOSakO09fGtY8mniS/1D2TvoJfHuUXEPejuVduJCayKm75W2pSO 7lKxyLOFxxWt+mqXgCF+zemAW11vkP/SwrXJCyBc0pxe0pgG+MwnE0glTbVX ozuWsbRFV9KoI3epWFv/Xxddho9p54LvsPcURvO16I83biu+rGfG6XzoPbgF FJa36ADHFqJROb0VBRu26eeeTgLuGfpx8ZVtvzi/rbn/r6Ox2PyTydIrGIfI 5kVJP8YSOnUlTdCXbaGxkmg01jVeCqaWt6Vj0OLFNHLJilzq+UtMluXRybGf osWddfL89tNn951yHWwI7D7ds7vF9a3p8j/8+Kdfbe36s5Oh3FO+/eeuvOUp yrlk3XsmuJeSLwkWyitloXcgEiwzR/tHdzvg6yOEye27R3fFZgufTx+50pdF +box3OzJw8P37+1zBEyUEcvE3lnoPuQzdY/uQTcnpKekN0l0tnBq6g05nlTo GttJ/ldE8vgMD6cOgvITPQZQVePTW4Li1J39sdmCEyEzfMG1DSLh0z2200bv BJjlpt4MpmswZ5TXTDySCdP1k6pnD4+Qvyg2dGfqUGT2aJ1Xzz5jXaO50LWW gWyKScf1gyzczNGOwSzMsR/EOMfbt/az/5WNZKC5yFzB5OT+Gp/B5kWHK3aF 6r2K9oDB01MHXzwsaOjG8G2wweJLvzexH25xYFyk0YmDWdA9nFfXKdQHMD9b S38W81cYZw2N+kT6hwz0X50m4x1BJXZbWudgQxtRdl0jeRiWSN/4dCiAgeMN m/uQAASdDp+ZomXx2/z+XdB22EGDg+yuVz858QaM2+lQBtSb+jNjc4U9oztr 6JliJzT34A70VCSnMjJYelF/Mn14bvrA6S5KTYY24zg4guiMDUP6fO4IjAnF LQoUt7iJz7uGa7iGa7iGa7iGa7iGv454lQczAzMOlRqPJFPdKdZ6JBIGZKo7 JadElrfLMiviUAE97CAE9ThcifXziHJdrPZiJhlZjyzvXycu6V9sa+PwVPan wC3exfhKOT5utbiST8y2mEMs0Z516Oe6HDPIsZymJetEyktWs5iv7KXwVPo3 D1/kJQjfuPxjyfW/PL40XtKWMp79tcctqvjQ1eEbNs4J61NpFx5baA7ehGUt xuNX9HXO/Rxk98mL2ebwd6tc+tJmA/FUaX3X62KxyPMXj58uPCnFBFb641fS r/T+FbtRNfb9VSVmzUL+qvjKtsB4Gfo+Peg7dmlbSZP+XPBdZqswHVYrJrAq uvQ1Rs4F3wEQHbfa0kEhR/hVuwRMikX5r0Dt5HQA0JF7zqLLaT+/kH7O9w58 vP0oBIbBLUh/taZFYgvIX2EqLUxyVdyo6xovjcSi8Jf4MXQhK7ry9SjxY5d6 /hP6d3l0zDnAgFiDOSfb9jjL8lqLci62vN3c8+2OS3/yuOJfPfvJr7af+daV 4J9cuPIn/T8xDH+Yfsnz7YZQjs2fafebHSGzBbPf48PYivGD+T2jzBdRhje/ sXcMI90mJw/wnGIM3Xxh99hOB6XbsgTYmxS9nqw+Q/c4Btw5w9lWv+RlGsX4 wf0Kf9U3gvxVS38W8k5+XWz+6M0J9DuqCeA5j/ZAFtIpc4cbwxl1QbEFPYUK ZHtwruHGyOyR3uu7oF5DucrrQpgEzBEU5x4cjM0U4ErwojAyNvOFVV6jhei1 0PBODCQczEHuqNMAMj2jO2Kz+Y3hTPxuDQiOgKl9UHLuqgtKuaTA1Kk7B2q8 JqR6QgLyaTNIJeE6DBois0ev396Hnm9+6Z0MpsZmjjYNZIFJTL51jWKadH4v NfdnIP1F/leYOx3NxiGtD4hz0wdA2BZI5K+gMH/VPZLLeQ6ltjoxaNSKydhz QGff+E7CDdR3MDv/xu19lBsNZxbA3uG82MwR6D7INPcRCzcGCvG1PzF54NnD I9XEQfG/i8FEwNcodBDXw2zhAPKHONEWXzoMnfR9AXM9khubK2wNb8fB8XC0 o+EVvG81XMM1XMM1XMM1XMM1/DXCU/FXaj4K6lWE29eDG1D/Lz1/lYp32mq4 ZYN4qmX4q03FVecFbInna6PwrcY7fVr8Fa9SVV1dNgC302F2FgoerHDqipvS PEMfxqKxuaeTA7esw3culLemUa71tOLL+tknd6LRaGisbO7xnZa+/1HenF7S nBa8Xi4xTnSYIOZ4d+rgUlPPd9HhKhorbUoHteeC71MKrEgZe3ORTvbIutT7 Lh8LWNGGOPtHVTp1dJJgenUHqm3s/x6TXU3d/6Xoctp5/3dAbOJRkDLAG8qd 20qb9JLjVpuODygsb9F3jSKH1n29rELKxAVN61gPNFrt1tdRDm2O1IMH6lRo 9/nL+cM/TBv9wb/z1f9poOHQU8tvLvziV/p/lOY6+37458aZH3zJf+rIxf6C 04GdJ4M7z4b2nfLudPhzHAETxcchpdMznstn81G2cOQl5qYPROcKGvsyYKgH xpCicQ1ks0yDF5246oIGPu2uZ4TzX2UqXpTwEeMHfZJfJQUYFnD8IDEzhd3X c+0hIzNIloDeGc6OzB7tG98FrbcN7IzNF/YOb+cc43bploKe0R1IU9MtDnQb 2/7w7qHoXP7ox7t4VQA+ObEP7ESCiPJEIS02cxTzbrGHp19s6s+MzBXcvrVf PjNRaBvKoYP58hwcpA/Gzxy9O3kQ5SklF8Uz5mN4o09oH8iVg/LkBGJE+MRm 3sTQvKDBGeZkWTiYbBUzWhS4R49VEOzMALHpqYOAj328R17ecYtciR9kfNE3 NYhUElyNcP4rCiqsC4pNsjz6UNGJkNaAvpUiMXuv78JuUsqsbgzSRMcw6MXk JAV40jGR7EYFt8AY9ozuBEkwm0cM85XhPBrYEmVI7fQY2jf0udZwDddwDddw DddwDdfwzxCeEMOVLI4vRSaKNeFa/OBa9SslIXgzVVlRv5LcT7Uels6UFj+4 BfGtY8mniwsbt06S4HyeXW2nvsqlL2vFYMB781djkWj4puOk961Pnj8ta9aV Nacfv6K/0vWfmaeydhwY+tg+cMtahvzV10NjJeSU9aSibVulU1flFPDMweb0 xu7/yn5cJY3sf4UeU9FoFF2hKJVWSaMuGkWPqYvd75W16iucBlKYznnYK1r1 xF8Zqyl1fJlLZ3MfHL1z7tnz2aGJM56hH0OjUw8l/gpulImpCBrcYiSqKp35 q67xUhRoTYNLoJ/TvF/pedfiMdp8pvpgpiOQ5QiYTgSzTvXkNvYV+k5+a/a7 v/7kv/2L+dJ/tWD5QsTy5ec//M3HP/nt53/za3Mf/X7Q998bA396rvWb568U +E5ktrXknQjl1gUwMbgzjNnRiSqR4sptPkwh3j+aG310lB2TkICSU6bHZvOj c/kLc4cilOTKERQ5f3vrYDafuAd/Qezu5Bs2KYe50DuWSwGGOYBwOF7f2B6K TJRi3p2D25Uc6ez/0ze+k+cdZNgjS0pXHhSv9Geg29VsfgRJmAMnuk3Sq8Mn TE29QUnXpbMO4ZbI7FFot46zLPqQ7uu/jhmc5u8fHry+Kzy2a+zmroXZo/2j eShD/4ITmy+cmNqPrmhgoZ8SXsE4jO+xy1nQob8oHDTg8YhBkRmqvhF0GGsP 54BV4TH0jGIqidy3cBiZum8MZ87dOxKbPwqNTk7uVZLPJ6xwifUiuokzt5On E6UcpFRXmLNrRCLuoK32sJQ3XuHNbAHyZJs5QqnXRSkL/ehuu89YFzLF5g5D RygT/lHKoo+TG5nPb+nf0Te+C+aX2EgDeehJh0VywgGmIlsGsrj7dlVqzc17 3jVcwzVcwzVcwzVcwzX8NcQ1/mq9+Kvir1ZZ1qg/5TrR+Kuth28dSz5NXOVf p/gQihuI13gMmKS9I72yzVDcqKtzHkSXqVik3l14/AomtnIOfXDsgu7nF772 8f02wG/cbTneuK2l77uPnkwWXzb+4kpakDgiTEXVgomnKp2Yw6rosoTDf0WX vlbSmHY28GdK/GBZc3rRla8fu5DGyNnAn0PThOuOXdompclqTi9p0pe1bKts 31btEkqbDUVNaQBWt2a19n4w93QiEluYetRT2pQGysta9VCJSvxVemnLNjAe bRgriuJ5heVQB/PgEjcajUYbe9+tcumtnZknvNtPe3af6Nx31pN/0fnHlzu/ 3en+b9c/+rfRv/m/Ise+Eqn457ETvxWx/D/RD78Y+eCfPf3bL0wc0w3/XLz5 sz/qLzZcuHTgTNd+TIRFrA55N2H8ILvTKCd6uK/uiM0dvXEbjxHsGc+NzRaO 3djbO5bXO7obPobHdsVmjty5+0at39g9nBd7dLQN+SuiFoMCxR5K8YNIf43s iswedQ3kOPzClYGcyPzhnpE9joAJ7q3xYQLwFiJkukdyMR/XUCanfqojeyxe obGfKKDxPXWdhjMh07OHeMLg1Zv7LvVk8esLPfG8JkdQhEbhEvoYB03QOzRs rhD9voKGanktgc6L3Zlw6ebE/luT+8gPKp9cqsw1Xoyh43MJ6zoFXm8u8lwK juy0hkTO5d5zdRePFR7U6zERm5QfGt0NH1vD26meB2Y7fGboQmM4E93JKNf6 mZAAxmPa9hu7LnZnV3npNEY6h1fxR+U4dM76Pvfg8OTtAxOTB8I39jT2ZUA3 +UWNwYCzeEQj+zCj/OAONGxkF8YnBjC5GRjW2pcJw949jsm4GvuyOIcY9BEe H5jNuQcHYRB6h/Og74BP3jkMGtoGdvBhkc19mUwDWjzo98vfldAQxg/OFrQO ZFk8kk+1fDbxJj7vGq7hGq7hGq7hGq7hGv564ZVu/Ad9wgWowN6N64zb5XrS OMHV4Rg/yL+Noa7glXSSF7elilsUqzp1UGc9i/L+deKSfrBBpb9WjptjnM8i XzPuWcwrxfanwrndtcYnynO0WjxBT/X69S/G36nXSfUG4an0bwa+FeL+Ng43 EA51UVX/LOBrih/c7PchPLOVLn11u67CaSy+ss0z+KNYNDb75HYx8T99N603 77p+fmFbdct+dotyhj8obtpW0fa1Zy+eNHjeOta47aT3LaahMI+6C2P3iDvS 3SC+6+7s8PHLaWUt2y50vQsfo9FoWbOBeSqFvzrjf4dyWKEP1S8ufp35JYfn AICAVLULle3p1c5sz9CPy5rSylpR5rz/vUg0dudRX0lzGpSyVn1JYxoltgIz 9CVN+mOX0qEJ5tCCo6VQ54jF4xeFKHmRXQ7/eXW74URH5kVn9qWLuRdqcztq dt+syxi360Ztuunq341U/N8viv9N5NhvvKj5N8/t/y7y888v/OBXnv1/n3/6 gy/N/fg3wtUZl1xvnunebQtlWv1Crd9YHxCZKukZ3UmheRgtaAkYOQ9VdC5/ auoNu98MMpG5go6h7eQFhKsC3t5w1+jNvQ6/0D2GEWetA8gmWb3owUUheIv5 2zHAcL6QBHDNgPCtiTeorrdQHirmTJoGMDeXk+wJX8vlo/dqfAama0CJxWPs GsZc8cTJICVF0XP4boFXOvJXE2/AvZjLER23DF0j6CzUN5oD1uKRlJ3o8WUN iZiHyq3DdeU3EjlWQE5K5lrkjjDDFfQalMBzDV1whjH7FnJrtM7BzvFbe7mO OaM6jd3onFbQ0pNV3SkSf3W4e2Q7fCVx3vWmPjMPL9zC+bi6x3eTzcZatwGM gQFc+p7nSZm9f+j25L5Hd/fHHhXEZijIkXX244B8fHufA/rlFaAtUAKjev3j /fxegikAY5C+my0AVdD35rB0ZCHq94iTdw4+vHsIvneqMI89tgs2R+YKL3ab 2d9sYHwvn7coxftLPJsRxgHnejAHBtzilX5LbLXfSxqu4Rqu4Rqu4Rqu4Rr+ 6eKr5K8qCbevB9cr/BXU1fyV0hbc+Ar4K4WP2hh8kRNbgb9KyoNVpeDTFLzG k5w3k+dOkOfUuLweNQ4VBU+lR7VO4nih15G/gkpSXmij8M3jrzg2inH2WtmC vNOnwl+xBrkIchE3Cq/z4bNGydIxQ/v0/LVYNDbwsb3CaShtST/p/QZ8LG/J cg9iUqxnz2fxQECnrsxp/PieE8RAprRFN/EoFI3FWvq+W9lmwMMKW/X2Tonv 8o38qLxFX96kOxd8X/aPMpS1bCtpTi+mVO18/mAJxveh/1VpUzr5X0WuP3DC jaeDb58IHKrq0A3fOQcKm/r/KzRX1pzeNvC30VhkePJMlVOARsvbkODicMVz wXf4VET4e3u6C7Dr91xwtbT56wDaPPukRru/Vec12/3ms8GdZ9z7Llw61Fmd d++jP3jx0y9Eir8Qqft8pPJXI8e/GPlf/+eLf/hi7B9/Z+Gffi32o9+O/eOv ffKzzwdsey53fvt01x5HCDWQxyNyLJL/1Xgevf9xnB1+LEyhTGAmKMOpELJV I7f2sB9OXVDwjWwHxDeCsWlwb2T2SM/YbjulkDrRbYrNHX08c/RkVwa/88M3 kLe5HM7k5Fp47t70oRPdGTbpvEJx6u6eyEzByS5TXdCAXNl8/vy9QpsUo2cI DaP7FlJMQTpAcLbAFd6BB+0F8Gw+h8ySQUH/q9lCPnwQLmH84EzBPLQVzEJv IoqDawxnSivKbwRrg1d3xeYOQ3eU7kcwsu8AfwNapJhBPJ+Rm7t/9+DC9OET 3VKjdXR4YnQuH4y3StGCBXMP8kHYEtCDbcFrecRZ5YE8JY8qcIaRx7MRecjf F0sfGSkmcXwXfVGaG/synjw8xI5PVp6amSPRuYJL/Vl2PjUyIPJRjCd6DOxP awkJE1NIfJ1EUwU5fnAvD9S1cZyRc90ZDimHlQij9OT+QeqR8GTm8PyDgzBB cMkRNMqOymgYzDXocQ1kUw464xKn3E153jVcwzVcwzVcwzVcwzX8dcOx8irj B/nfeW2cEUUVZxefslV1SzCFqlXgjuDGxPFtVPzgUmvXhK9YVnmjFj+4jPxW xbeOJZ8uHlc25L0k45hYvrYTefgKF+aGavC+zRTQ6cBblS4jJjxv0s09nXD1 fzD/dAKujEyer3LpK9sMZe3G9sEPnj6exHMDWw1nAt98tvB4/pOpuo6ssla9 pSNnaiYQjcam56+VudIqW/XlTYbzoe9IgYGUvz180wYN0YmBLxDG4w7nHZ79 4Vt2Jr5u3G9/9uIJKHkembd6c62dOXNPJx/Oj1rcWQ3e/Q/nroFM6+D3qjp0 lS79pZ73b9x3svHPX8zdnx9xDfzN6MQlpqqmZ4dB5fCdC86hD6bnRjFb18Iz DNryGyjPdkZDiDJfhf/Y1fXujWNZz//7r0bq/+2LVjFi+fcv/ulfLnzvVxaO /eHz6j/8pEGIHfvC3Z/+vtv9P1p6//Rc6PCJrmyksCgdk42ZjdlC5K+ClEgq qKOs3YIPPW3yh67vshOF0juGH7vGd7QN7IBLLx4dmX2QfyaESvpHcxdmjz6e Phi8lts2mPnx7f2xmcL5hwehAh8Dw3nPHh599vAwEV9IN3HG+Id3D7muZjvD Wbdu7Y3NF2IC+YC5wSe2DGVCQ88fHr45sR9sc1/d8ezhEZC/1I9819ke9ICa vruvY2hH62BO71jeFcCDBtdATs/49rkH+ZxsCrpzvicTkzXNHYbbn9w/COCZ Pkw73zu6e3Jyv390p7N/O3Tk2aODz6ePnAghoRca2dE/shdaf3z3CNhDnJXQ MpQj5+ZC3zNKhJ4/ffcN99VcMODmrb3R2TfJfQsG0wxXIzMFTx8eBbw1nA3G L0wfhuFt7MuAUT3XmxmbKZDuHcgC8xr7zJxJ3hIgPt8n5blCJ7S5Qs4Djz5j wQz03Zo5MnRjN/JXAxmR+fynj47AKA3e2NlCnm9MeU1PHfQMwRzl3L69D8yG qeFpxVxYc0dh+sBImIKTXSYYlodTb3iu5sCNH0/sibAwPdSBYUxHdv/uQbAf rsIowSRe7M6EAZm4+wY0Pfzx3r6RndAK+pgFDZv5vGu4hmu4hmu4hmu4hmv4 a4wrmb0TUoVLH/EsIaN6UxmfCXyJ/s8ibk8kQ1bC/YkEzvrt2ah5X7ldcXl5 ad79iWJJ+c9lcBvnc06GL5VXtxu/PsUU61BMYX8qfG3zsmH8Zyr8JfKqra+e qix/b+o1IG4SL7qx56Im4FavkbOmV7UZShq39V23R2OR+U/uVDp1pS3pJU3G 8hZdz8fWmcd3YnSU4NnQNyhTejoI1Hv3RmOxBu+bZS70yDrpf/v2dNfzyJOp R13zn9wFPWP3zts7t5c06UFzWbPubOgdCgxcKKeTAYuufP2M731mtDqufngm 8N7Fvj+/2P0XVycuvnj+OBaNWd3Z9x5fA4Hp+WsO746SNl2Nc0fvjdKFyNNo FBmuuWf3at14amF5a5p75O9u3G9/GplbiMUc7dkjkxefLTxmm4enzpY26dsG vz/3dIKZMfjTfvW7GDTXYYzzY/SIZ3r3dIT+sqvkwCc/+b3oSfOL6rTIP/xB 9H99OfLBP184oXt+ybRg+eqLos/fKf69jprdF07ln3EWnPbub+jcYfVhBnj0 v6Iz9eghNdf60YHH4RfGbqGnU2h4F3ouwRQHxUHKghWbPUQuRgcb+7N5xjE8 kNyKHj84sjCTvzCL5/ed6DLCX8wTPpv/fPpIB3EdGO7nQ5+9wHDuc8oEFZk9 GpspHLq+y+LV13gFh9/APEznte2TkwfgUnQOs4tTridzlRddT4PX8p5NF0KL C3NgCaa3qnGbgiM7KRU5mJcPl0CDM5xNnE/B2Z6Mh1MH4WpzH56p1zqQNX8f rYrOvokduV9woSuLSZgJaBFunzscmSuIzuVDuzg+aE8+qKLOmqs7RO9QDlJq 0Mqjo7H5I9fGd9l8uDgtbh0Le4d2TE7sg9tRydyb3VdzrSHMgl7ZKfiuYsel xOkzBXQ2oghrm2LJyW/Kg/F6HLDZPbwbLvH6v9KLcYgwJvCxsRcJwPbB7dcn 9oKe4MguPh/QO5j7yfQhzGw/9yYMbP/Ydnr3gnKxpScrgrOch88a+gmbLoez YRwAhC6AcHhsT41HZw+a6oJojGco99kDzDNGefsLe6/vaqEjDjGBP2XyhxIc 3t7gE6nvG/W8a7iGa7iGa7iGa7iGa/hnAZfi/miTWNFhgI9xOMmrcahXtUu5 XilO0LhUz7J4XLwhn8qUJA4xhfxa9St40v5uAB5IYX8SXK8a//g8YMlxozqf mKJHPY+p8o/Fz7shqf7l8MV4TCyI+8UE/ZxfS2nXRjhUlJjEBFyJtUyFwz5I wWHjrOgBHD4ubRcqip0gI+F+sZpjIYnUWoonkaf8YDJuXCUu2SnHXcLWbK35 zVLii3X1OKTELd7FeFWKPRSWx1PHjSbHl9Ev1yWc2UgFh48KDuNT4xWUuE6W YS+dteIb9z5M5K+sfqPVayx1GTl/VGmLbu7xZCwWG7htw3zpLbqStrTyNv2p gJTe6v78SE2HvsSpL2nTVbn0FU7dvbmxq7cvYHKqdkOpc1tlm+F899uXw+9d 6Hmv3nsIHZw8YkmrsZiSVp3r+nNmq0BneRsG9/388rapR12xaOyU771jjZg7 C/SUNRuKW9Mv978Pq73UqT/f/W5DMA9GptKlB1OrvTqw4WLvuw7fEYvHWOfV l7dDScfoY7cBDLjS/5/xKXMLVR3bz3e/c67n7Rq3qdiZBuaBMed63rzQ+069 bz+FrOI4VHrSrej4JNZ4TXZv1llf/qWL3x48Zn720W/FPvpy5Adfiv797z23 7Yj+9Ncipb+zcPJrC3VfWaj44txHX5z+yZfHfvZHncezL1j2njq/t759lyOY TfGDeHwenjcXMmEkrM90rtccncPz6U52ZVAedQNHyJ7sQr6rSWaubP50Dl6j 7wikSloGtjf2oaOUBZZowHSpPwfkMa+7F0MLQazWb6z2GRwBEzpi9WWCqhO9 InMmNT6Dza+X1jnlsGrsF5t60XPJHsLXOyzyyk4d9V1o6s1q7DE3dBnpvYf5 /EH/1OTeyExBZafA+ZrghQyvX6TTQ+K5riyrT/lO1J/ym1wDmZcHMio9abjG /GZoAt/hnQaKmjzAMd3sbwz1csxVhf88VOum9Rk0tA7mNPbm1PmwIVj2/J5n dylQAnUYh9ZwttUPl/ScCx2+dCoxL5YAY9LYkwn2oJ1kP9mA41DhSa/w6JlU DF3NxVcQRfC1DexYIMP4PV9F71VQeyKUUR8Q2Ye50mMCU1sGslz9WTDUYAaN pwCDU+7VQR3fjR3Gqs506CyOuVt/pje7pT/rTMhUJcfagyocN0861HGuezMa 0IMLTYU+do0ihwl4hQf6S55joS33e0nDNVzDNVzDNVzDNVzDP11czUdBHYoN 9w5GCSd5BV8qn5RHWgav6NBxaotV81Qbw19tFk7js0r+Cvk64lVWhyfXA3OX Cl/lPn1lnPcvuNfAfQTiS/irhHVlI3w1PNUq8QQebBk7GVf4JWmv9Gr5q/Xw VBvEX62Vj9okfEV+bKP4q4SyYX6n6NeHibZqOvS17UgonfG9HYtEY9HYmdA3 kEymdVXdYapy6R8/nYpGo6HrP6tBhyXknzGK0Kkb+tj64vkTa2cWLWDMmYYz 5cfBsfp0dT4DTrrbAMLlLTqMH8SDDWPVzvQqpxFKmctw/V5bLBa72P1eZau+ qk0Hb1qwp8ajQ3rNg0RNnQ/TmIMq+Gsjj6NanxlaoYoIrRAoUjFaPPq6ToFO u9NZOjPgI2iweOkv3NKJ3ko1mGDNZPUZ+IC/+pA0yPX+rIuB/Cvnvznwkf7J 3/3Wiw9/feH//T9efP8LC+W6T668Gav97YXqbQu1wosfffFqqbm94VvNjjeb 6g811b8BpfFk3unLOxo6c1zhHZF5PMzOEjKQv6XpfI+ZTuXjoDl8linFt8h/ HeRGhWmRvCZ7MMMSQHIGwYDeGhL5obZTJjQ7pdKCuyjlO04f3GUNpNtJmF8R TNqAgByxTmcgUgdxGfgw3TpLonk+AYmsgAH089uPc6RDvS6kc/jFian90bkC h+wASTmyuBWkp1iPql0Dpy6HSw5aWrzAYrOFmLWengjmwdASSsZll4eiwWsm O2XPQ8ppz05xePyf2kHax4iU6UvyXJUHRPW8YJ2+dvESJlGfOdI3toe6ifTR zVv7YvOFME3SM8Lpp+B2vx7/0r8xKaF8Upg/kYrcrt0n1FPrHLnPIwN9oVxn 2LQlYCSF6HrH7nYWHgFiFHlwwIze0d2R2aOtAxkqL1ndhj/vGq7hGq7hGq7h Gq7hGv6ZwpOBKjzxrpXkf2lwv5g8Z5EvyaCtV/9G4Cu3K65K3p8opl4h9o3G U/dL2eksGfkluDoA9iXn3R6PJLP/5fCXiB98GTxVUeSXiRqOn7vkj4N9Y/Kn LbMe1okjm0H8lcVjrHIK9b59Dx8P4/mAsdi5rrcsHn11p7GuE4+Zq+nQD03a MC7Pvx0QkLd4hWp3eo1LNz51LhpdGLl7qd6Xa+k0Wb1mDLv2ITdi9TLvhAfD Vbr0Fa60893vc9xflWsbgDUdxqoOXXP4u5jjffijCqehymmsbtfVuAVoxRrQ szcOck1+oyVAWf29BjYbiQu/ni5xtn8z9YVOAQABrJjYQ4YEkPXC95IPLDTy 7eg+hG5ylHg8kFEf2H42cKSpIX/yh79//5++Ol3xHx7/w28+/7vfW/j7r0Y/ /OJCyZeel/1G7MNfX/jH34j8zy/0H9vREf6L8+EDZ/v2nu/bd757z9nQnpPB nQ1BE2f2npo62DO6Mzy2C7NXYVjfkbGP98kPOPJFDiSLkOtgfoMdh5T5Ij5K Mgx7hESKWbrXb2ZJO1JGxDgRT8JvY3Tu8hGXFTTZiYRhgojIIh3faAkY6/2U Ct6vZzaJGSGbzGraiW+Bdp3hrNGbe5lNqgsakPICM4gcw49ELhFlRCyZygyp O8TLBYZze8bzOBUV/D3Xi3m0/Nd21AWZblrsOxhmV1gy4oVAoJbukhI8koX8 j0HMlcH4EF9HNsu8X31AVJ5c5vEwafz80fGP90CPOoayb028EZ3LX3hw9Fyv GROUQXeoXzSeBroRxsHMhln9gsI0MqMFH6EX3WM7/KM77KpnlteSJcSPrYGo QrrFRzaH9A4Sk06cpDDSM73Zg+N5FDoqSS6lrLfc7yUN13AN13AN13AN13AN 31q4vI+I/7h+/cnA1whPUcRUG/YU+NaZ36V4nMBnib9aFl/bevil5a+WkX81 /NUGnouagHP8YJnLcDL41uRM7+TD4NSjnomH3XdnuoYnHGUd+iqn0eJFjya7 92D7tb+t86F8VTuG6Vk8Rrjl9nQX3DL1KHRvtudU6M2qdt6qGynWTE+RbsZS Z/rx5vQql9438mM+WLDGjQ5+eNpgq66mwzh859z9x0MW11731b+dmuu+cb8d TIJ2YRwq3WK1O51ZArC5woOBWhx7Rf6ooj2YUe7WVXrSOdcQ4hirJXIfwVSM BfOba9wm9TmzlVLdXIXxg6Z6f9aJ1rwL1t1tZZmtl7/t7H7P3/Xd22VZj3/4 r5///EvzFb+7UP3FWOVXHv/iK3f//qtP/uevP/jr32ps/OaJ0C6r34ST5RM4 vs+GnA+mbIrMHsVkR8RcPZ4+1DuWJ3kc+c2OQIaycpDrCOoox7vZGjLV+XV4 /J9PWvPMxXHfyZ/HxPSO1S8oODueIQHl18tnXOLtUKnx6dkdCPnJTh2vT855 ZZV9NaH7MGjwscIHY6unwwfRQbTcjVRVXVCEOkwB0lZ+I82FnmkZEIaPFN9n WDzP1w8VEe5lFgjHv4O9iXASYZrsQaKSZvMn7xykEYB79RU0XxxvCOuHSCT0 WyafUmTYYIXAR+K7xIoOdMwjIssM90JbOP5BzGNW5TFZ0GnNWNapJ/uxL+QX rXdhHvg/5kMGMSXXo4L7U0fOU7Akx/1Jz4gf9de2GykeEHWSfyxSeRw7yUwd 1Bt7sqOzhZOTB2AAYU3aaLJgQGBY5OdLD6rIn02gdUt40FDeKcAQsQzYCebV B5CehYGqcOM8bujzruEaruEaruEaruEaruGfBby8HVOp8CaRcqfo+VjA8nYj 4iQPdcCTyktxhSifqEfBlXhDRd6Bv72TxC3aU8Qzfuo47wGXxXUKLu1fVONM eT82ax7j4jE3QL++2q1X4ZIfwvJ6uL9QUe+L14or8YNL5ZV2lfhBMECJH1y0 R44fZHwx3nAZvFOnwg2rxNm2GjmvC+6FU+NKPB3j7AaWEvcs5pvi+MpUOOvf qLjFVHF/a5VPqQfrehnXK3nC14qr14P6uVs7noK/6tCXudLq3GKt21DWqitx pZMnlZHehxyyZ6ygM/5sPqHOJ4J8hSut1o8UVpkLU1RZ/SaLl7gCF57lZw8w J2AkJyiUqWhLH5qwP194yunT6zoxQLK4XQevR/Tj8hj6btXHONl6LHZvfrCk A8bBbPfpiSfhZxOfR+Qr6AA45NDcUuxYlYfePz545yBhVd0hLj6/7nTsY4hy ELn17NzCzxTq9BtrPDqY7hO+rDOt2x2uXSf8+0/37DrVnXep8xvXP9LPfvTl Xkt28Ow3pyp/J3L8y4M1mZ0tf9FfsXvq+7/rrcg9Gyh0+Myc5wqdoIhTOtFl bOnPag1vbxvIaR3IOh+iwDR25qFe8PyyG5U9wOy0mUkSijuTvH2YsJJ9/wyg nIMEcaj9JnZVsoeIXfShMPpE+SjGlnx4YAZ5HVpDuCAxFxa1XkP5ptj1C+aI eC1B4YWYz6Fxg3k01QUNFZ50fM8EKVdYZzpyg35jfchUybmweI156P1J3al2 S993OM4dpgoPRdj59dIc+Y2N/dl37uzrGd3JQXmVxEli3nJan1C4+/J7WJT4 McRFZQ0wDjYTL2SAeQflFW5RsUF5h2M4qsdwssvUOpBxpSf7cm+mM5x1ti8L lNRQf/H72q2jdpE+qpTWLU4Z1OXvO+ZO9TzO8C49H8qcmNp/9cbuqnaB+D1+ 1nAobDJ3h88afbfSWhWZ+5LzDKCnHNyL8rQkYCLgo51cvDbueddwDddwDddw DddwDdfwzwKu4p3EeN5pRf4qQT4lruav1Hrw97BPsKl5Mxn/bPBXjHO/KhLz ieni2l12vipT8FQV9O/pq+evVrdOPjX+ahk8WbsJduplO+N4LYV3Ussr/BXs 0V4Bf5WAK/xVcnzx3hX4q6Q8WFUK3qwqBd9VvRLvpNYDFUXPp8VfJZQN8T/k UC8OvkOvKjzGToS/tX4DH2nHQU8Wvwlj7vAkVnQxsvuMUryez8QJqer8Olun SJmp9Bypx3PETBF5EJkwRNFrqHVjudDzjcDNH7EfF5RaJNDMFg8O2qnAwcDN f2oJ/ycp/NAvcBpt9kmT4sUwuEyiFKSGSEAKv5LqEtVjlw/upHvNHHxHPJK0 2DiJutVvqu/KcoQyHSEzPB0NPvFUz94rl96+/9M/6Lbvbuz8dnvvd/prcp4W fd5Td6h14M8u+99qOfnHfcfNFy8eOhPaKWWU4sxRUpojfFrt0lCLOIaykZho PWCyhhaPEKV07oqwVFHupY5TEGWQ8q4HDHLcnBR5p2SUwpEPSItHGgopK5SZ e2qloZP7LsrDIjn7OYIqL82gRO6hHxchDmmg2GCB+8jJzGlgEaczAQX1wLLB GMRH1nIydikoL7QY8IhTGdArZjBulwcHl1+Ig/jiBgoH0y/IfTFzcF89rwRi Avl2qVFqCEk/DtiUF4CUsItb9BmVEeC7pKs02qoTYJmQXFxvDr/AmqV596v9 MGk1YpIxCmKVFcqLVp5u0sbk1dKndQv4J2u4hmu4hmu4hmu4hmv41sHllB30 Uc4XpPy2VP8WTSK/rJ7Fdu3BdeJx9ifr1HLyG4Srf42rf8bLu9TE8VkmkGot +KbMbwo87uoy45wgpmwz1XdtFJ66X2IKOxfx+HWVBE/syCrwuF12UExmf0o8 RX/j8TXGDy61dkPwVCWpfPzcpVxm6hm0rxOPazHJInkpXCTCQeTANC5W/3Ly MoO0nLzNL2/bfVgkooxoK0WemTEU6DRgzisvCzNRKWU6WmW/pIxJSeQT8MQ5 Uq9MIouyLvQc6LDs7Dy960pv4emeXWf79nec/eaT0i+02/Mv9h5s6M4+2334 cssh96Xd5wO7baFMpj7kvEyGFCvh1ZSk61B+scj5xpOt59TvYZWSxPFfcsvm rE8N13AN13AN13AN13AN1/BfdnypzIp6lt9PUUph47rt2RBcvT2RTFLhiv1q O1Pv+17WHvtSPH5vvjo9qeRXhauKmFCxJ+LCunE1TbSy/BKeTXHGsMavH+mj 7NOyIh5vT7Ilmqx8KnjKefcnEjgr4EFxzfaslRddf3+XY6Ht8StkGby83VjW Lq0QqJR3SJc2Eu+QfBplXFhRXsFZZhkcYwxdBs6aDhXAmbxS2gW8xKmHS0Rz GZfTvwp7Fu3vECrkWDb2I2UHGLV/46KfYUCglPXmE6GMsx17Wy/uPOND9yoK Y8xu7PiP94v+qPlE4dnQPsw3FTKf6tpxwb3rnDe3PpiJ7jpE4rGPkJxSHkvS J3GVRXZmW1pn/cgdMTfIdYtX4PxXtiR+fSo/RilmOaV/qeIfS3GFav9bgfNK qeZFtKlwR1Bc7XxpuIZvVTzZOtfWs4ZruIZruIZruIZ/mniptJ/Cn+68b+J0 uGUqnGVYvkyqC0nwdl08LqwGh9/5S3Gl3TL1vm8tuHoftxzeoVfjyfet6v2g nAt3tbhKT3k7HXFFOPwsZIoglTxslBZ/N3ZgDl7esq0eV/RAsdM4A8h1woX4 uMX4OMpNxjlutELKf4J4pSpHShI8kEI+FZ5CD7ebJP5xjTjrr4zLx7Wh+JJ9 9GrwxbxexEXA3lyW16v1q/BFPXCvGk+qR81vrAdXxUXWekSqi9zuIi5zCwm4 ci+/x5TntEzmDTYSV70H4t4bqeWV5zfpe6ZMvnfpe1itZykfYg+Kip6kfMiK 9ijvE3rnLL4rFP6K452TrQcDzFFD1/ZL7dtPduZZgzlWvwnzSnnN50Nvjn6Y ecV25HRon9WXYQ3oKbYxq8GLaawozE3gc1ftclSm7fXnrxLeY8nmfaX1sNnr VsM1fBPwZfirLWWnhmu4hmu4hmu4hv+S4KUqPor5K45RKluCs/zL4El5MNj7 LJVnO2Xeaf240m4cruLTUvFXZerfaWo8lfwaebC4eUm+39Gr+SjJN2PVuIpP 0zNnJeHtUg6orcZfJc0/ZvMb19luKh5M5otS8VFbBV8Xf5WYH2wt8lUeIRWP oeKjkvNjSXE7nVmQir9SeINUPFUqXF3scnldcGu8C+gK8nI8muJH6kjMerQO exLaFRNvkRoV+QRDPIvQl9UQyoGmHZxiPWg6233QXb7rvO3A2e43WJhzLlHa KFlhfGz10rl7JUVM1vriCKgHKkFmQ+IHN2K+NFzDNVzDNVzDNVzDNVzDNTwR XyqzNe185XiyfcpG6V9PvpRU8qvCVUVMqNgTceEV4euMU1tru2vVv0Vwkf1Y Vo0nWVQrtPu6xQ/a1CxQ/POyUbgtvnXHkrx8avmlWdGWeX6t8Q5ICfrjhoUI 8KTyL9evpfxV/KtD5q9slDYcWSk6QrFOIdyCptNdu06f3nvKtvt0z15FucNv QO+soHSjTc74/cvMX23S+tRwDX+VuLaeNVzDNVzDNVzDNXyr4bb4+tKyVP4z iceNj39xC7NRv/cSL2n8VWD1/EkqO1eyf+N5mE3BU09T0n10SnyT8/+/DL4x /FXZ0njnJX6YL4unindeSV7GhWXwUqgvK580njq5/FrsR19Tl45fWVApb9cz vySd90oyfJ4p24D+eO50xms7jZWd0oxUd4oO//aGK3tONew8Ecit8xl5jmr9 BorXw+WnTl+/1eIH1X6AeM6pdOapqI6jVJ8bqx4f9Tm5ycY5bvxVfsUrzZeG a/hWxtf6/tFwDddwDddwDddwDd9MvMRpgI82+kfz4jYd1Dl+sLQtEedtyFKc 9cC+bHkcfs+nki+R668GX2Zfmer3WzwurIjbku5/U+x31Pm4eI4I1y3Kt0v1 9eFK3i0A4aNN0m+ocOrsKhm+FyqVLinGkPdrm4JLub+Ww3Fs/Zj/R6XHqJJP hcfpkeIK/WLS+ER7irjFV4bzGkjA5T31YhyfIyimwjcvDpHX9kbGM7qlGFs1 byDlGVNwWSYVXkrP2tLndCPxZM/18vLK+4Tek8YV3zOrxxP2j/QeW4M9i/qX 568W16dOmceqTnw/1MEa6zTUugV7CCmgKo9g9WU5XHknL2+3+7ItXoFzXtX6 jbX0wEKxEK1kf835q6XvMR43HnP1OCe8z0tc6cnnd7PXrYZr+Oa8D7X1rOEa ruEaruEaruFbBy9uk3keP/JLUDh/+yJPJeOJ/JVfVPNaJTI3ZY/nrxR8Gf4q jh9biQdbB16ShNcSkuCu9I39vVcq81f2oLj03zG5v8lw3v+mJ+Wj1oov5a/s 8r5YzV8hryX5t+heBld4JKgn7PtsnEO+fUX+SlzEX4q/StCjV/Juqf0o1oq/ Sv5K7QeyPK7K95Uk73QSvmtZnor1JMXV/MaK+GbwV7ZN90cVlcJsjCNg4mla pfxKfpup5FV4vJ2KtQqunKC6pv7KrSf4Z4rqq3HGBGH9m+xBE7/BMKQRqSpc RSd8OfbWLEcwG08bDGAqeOyIHGMoqaJbljTxKouYrPXFEVBAe/y4oUyq+FyV koRxVtaJWngT1qeGa/grxbX1rOEaruEaruEaruFbDbcl1JPlY0mQX43+pHld lsFX1P+S9sj4ivvNxH2l8u/7q8NXttMWZ8maxieV/uVw1b5M3XRcRTU4cfLr wO3BxH4thyePO4sbTNIvKhtPpZ4KT9DDG/BEO+Xt9jrwBPs3BE+xx0+6AU/A U/EPKcdzFeO/qnlZI74MG5DweC6H///mgV65 "], {{0, 0}, {1600, 30}}, {0, 255}, ColorFunction->RGBColor], ImageSize->{1600, 30}, PlotRange->{{0, 1600}, {0, 30}}]], "DemonstrationHeader"], Cell["\<\ Probability Densities, Expectation Values, and Uncertainties for Gaussian \ Wavepackets\ \>", "DemoTitle"], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`a$$ = 0.3, $CellContext`k0$$ = 0, $CellContext`x0$$ = 0, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{ Hold["wavepacket centers"], Manipulate`Dump`ThisIsNotAControl}, {{ Hold[$CellContext`k0$$], 0, Text[ Subscript[ Style["p", Italic, RGBColor[0, Rational[2, 3], 0]], 0]]}, -4, 4}, {{ Hold[$CellContext`x0$$], 0, Text[ Subscript[ Style["x\[InvisibleSpace]", Italic, RGBColor[0, 0, 1]], 0]]}, -1, 1}, { Hold[""], Manipulate`Dump`ThisIsNotAControl}, { Hold["wavepacket width"], Manipulate`Dump`ThisIsNotAControl}, {{ Hold[$CellContext`a$$], 0.3, Text[ Style["a", Italic]]}, 0.3, 1.3}}, Typeset`size$$ = { 900., {287., 298.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, $CellContext`k0$229972$$ = 0, $CellContext`x0$229973$$ = 0, $CellContext`a$229974$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`a$$ = 0.3, $CellContext`k0$$ = 0, $CellContext`x0$$ = 0}, "ControllerVariables" :> { Hold[$CellContext`k0$$, $CellContext`k0$229972$$, 0], Hold[$CellContext`x0$$, $CellContext`x0$229973$$, 0], Hold[$CellContext`a$$, $CellContext`a$229974$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> ($CellContext`delx = $CellContext`a$$/Sqrt[ 2]; $CellContext`delk = 1/($CellContext`a$$ Sqrt[2]); $CellContext`p1 = Plot[Abs[ $CellContext`psix[$CellContext`x, $CellContext`k0$$, \ $CellContext`x0$$, $CellContext`a$$]]^2, {$CellContext`x, -3.75, 3.75}, AxesOrigin -> {-3.75, 0}, PlotStyle -> {Blue}, AxesLabel -> { Style["x", 24, Italic], Style[ Row[{"\[LeftBracketingBar]\[Psi](", Style["x", Italic], ")\!\(\*SuperscriptBox[\(\[LeftBracketingBar]\), \(2\)]\)"}], 24]}, PlotRange -> {0, 2.1}, Ticks -> {{-3, 0, 3}, {0, 1, 2}}, TicksStyle -> Directive[20, Gray], Filling -> Axis, PerformanceGoal -> "Speed"]; $CellContext`p2 = Graphics[{Thick, Blue, Dashed, Line[{{$CellContext`x0$$, 0}, {$CellContext`x0$$, 2.}}]}]; $CellContext`p3a = Style[ Text[ Row[{"\[LeftAngleBracket]", OverHat[ Style["x", Italic]], "\[RightAngleBracket] = ", NumberForm[$CellContext`x0$$, {4, 2}]}]], Blue, 18]; $CellContext`p3b = Style[ Text[ Row[{"\[CapitalDelta]", Style["x", Italic], " = ", NumberForm[$CellContext`delx, {4, 2}]}]], 18]; $CellContext`p3 = Graphics[ Text[ Column[{$CellContext`p3a, $CellContext`p3b}], {2., 1.7}]]; $CellContext`x2plot = Show[$CellContext`p1, $CellContext`p2, $CellContext`p3]; \ $CellContext`xplot = Plot[Abs[ $CellContext`psix[$CellContext`x, $CellContext`k0$$, \ $CellContext`x0$$, $CellContext`a$$]]^2, {$CellContext`x, -3.75, 3.75}, AxesOrigin -> {-3.75, 0}, PlotStyle -> {Blue}, AxesLabel -> { Style["x", 24, Italic], Style[ Row[{"\[Psi](", Style["x", Italic], ")"}], 24]}, PlotRange -> {0, 2.1}, Ticks -> {{-3, 0, 3}, {0, 1, 2}}, Filling -> Axis, ColorFunction -> (Hue[Arg[ $CellContext`psix[#, $CellContext`k0$$, $CellContext`x0$$, \ $CellContext`a$$]]/(2 Pi)]& ), ColorFunctionScaling -> False, TicksStyle -> Directive[20, Gray], PerformanceGoal -> "Speed"]; $CellContext`m1 = Plot[ Abs[ $CellContext`psik[$CellContext`k, $CellContext`k0$$, \ $CellContext`x0$$, $CellContext`a$$]], {$CellContext`k, -13.5, 15}, AxesOrigin -> {-13.5, 0}, PlotStyle -> { Darker[Green]}, AxesLabel -> { Style["p", 24, Black, Italic], Row[{ Style[ "\[LeftBracketingBar]\!\(\*OverscriptBox[\(\[Psi]\), \(~\)]\)", 24], Style["(p)", 24, Italic, Black], Style[ "\!\(\*SuperscriptBox[\(\[LeftBracketingBar]\), \(2\)]\)", 24]}]}, PlotRange -> {0, 1.1}, Ticks -> {{-10, 0, 10}, {0, 0.5, 1, 1.5}}, TicksStyle -> Directive[20, Gray], Filling -> Axis, FillingStyle -> LightGreen, PerformanceGoal -> "Speed"]; $CellContext`m2 = Graphics[{Thick, Darker[Green], Dashed, Line[{{$CellContext`k0$$, 0}, {$CellContext`k0$$, 1.}}]}]; $CellContext`m3a = Style[ Row[{"\[LeftAngleBracket]", OverHat[ Style["p", Italic]], "\[RightAngleBracket] = ", NumberForm[$CellContext`k0$$, {4, 2}]}], Darker[Green], 18]; $CellContext`m3b = Style[ Row[{"\[CapitalDelta]", Style["p", Italic], " = " NumberForm[$CellContext`delk, {4, 2}]}], 18]; $CellContext`m3 = Graphics[ Text[ Column[{$CellContext`m3a, $CellContext`m3b}], {6.5, 0.85}]]; $CellContext`k2plot = Show[$CellContext`m1, $CellContext`m2, $CellContext`m3]; \ $CellContext`kplot = Plot[ Abs[ $CellContext`psik[$CellContext`k, $CellContext`k0$$, \ $CellContext`x0$$, $CellContext`a$$]], {$CellContext`k, -13.5, 15}, AxesOrigin -> {-13.5, 0}, PlotStyle -> { Darker[Green]}, AxesLabel -> { Style["p", 24, Italic], Style[ Row[{"\!\(\*OverscriptBox[\(\[Psi]\), \(~\)]\)(", Style["p", Italic], ")"}], 24]}, PlotRange -> {0, 1.1}, Ticks -> {{-10, 0, 10}, {0, 0.5, 1, 1.5}}, Filling -> Axis, ColorFunction -> (Hue[Arg[ $CellContext`psik[#, $CellContext`k0$$, $CellContext`x0$$, \ $CellContext`a$$]]/(2 Pi)]& ), ColorFunctionScaling -> False, TicksStyle -> Directive[20, Gray], PerformanceGoal -> "Speed"]; GraphicsGrid[{{$CellContext`x2plot, $CellContext`k2plot}, \ {$CellContext`xplot, $CellContext`kplot}}, ImageSize -> {600, 390}, Frame -> True, Dividers -> {All, False}]), "Specifications" :> {"wavepacket centers", {{$CellContext`k0$$, 0, Text[ Subscript[ Style["p", Italic, RGBColor[0, Rational[2, 3], 0]], 0]]}, -4, 4, Appearance -> "Labeled"}, {{$CellContext`x0$$, 0, Text[ Subscript[ Style["x\[InvisibleSpace]", Italic, RGBColor[0, 0, 1]], 0]]}, -1, 1, Appearance -> "Labeled"}, "", "wavepacket width", {{$CellContext`a$$, 0.3, Text[ Style["a", Italic]]}, 0.3, 1.3, Appearance -> "Labeled"}}, "Options" :> { TrackedSymbols :> {$CellContext`k0$$, $CellContext`x0$$, \ $CellContext`a$$}}, "DefaultOptions" :> {ControllerLinking -> True}], ImageSizeCache->{945., {380., 385.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>(({$CellContext`delx = 0.7085209947489206, $CellContext`delk = 0.7056953904057359, $CellContext`p1 = Graphics[ GraphicsComplex[CompressedData[" 1:eJw1lmk0lQsfxTmG4+C45+YWGaMkisosPP8nMnaUISVRlCFjChWuMVLmKWMD QqYMSYX0PIcypcg8ZDjmIZIx83vfte7da+211/66P+z1E7l6w8iGwMDA8Pof /z/n4rk6d3bIuLuD5PD9alngl09bvZnEgRcyCPLqO1+AK1nrEoJbbHjtY37R 0Q5PqBgTdGaMZMWFdPjS400eweEVEk3oMDPufLqq9ldtAZR2fhDziGfElTwH qBzaNMjk8lQgndvGMu5SjS8otMAfFFaNFJ41bIXaq7Uk3AsvSg7cfLK4iKlR M9TLl4agdzw3QMxgDhMpCC/tX6UDnidlvTQ1gk1z5PmbaQwC4XIu91n7duzE BCWU43UnJLkNGA8QEzBidvfO50+foYdrojpUqw1iFUsDya8qgL/66q0xzRGg 2la4rF3MhhvvpdH0t7MwJHSh8uPlcJCvdLRR3VyEgoPFAsrTzsB8V5qk8PE3 FLZybNuUUiE7/kpY1eIWmEilJIgt74eIBzse9jaM6KWhtpKzrWtIye37uyuZ mVH7bLvmFLM65EP8qcy2RFY0nljrnNgdg7weVhYt3WZDZbxTRF0CzZB4S9uo i8kcaKlUUSzRkA/5d390ZJNIc53uVWO26RpXauLEeVwHM1BGLVBz/hJdp8eO t3JF+9Wr20O4ZvjpqE9EXCFvo8SY9QEszHLzRJuz4PLfVDKqptLhhq31YsMg Adf7++si28gbIBT5DKleYcAT50beXFWoB7Mo7P23sg2sJ2Qla0K0A/osd/em Bq9gCw73z0qFDkBo6yZvd8QvjFrW0OXZQ4cv9TMLnIJTWGTQr8iXcnSgXSTM pQoNYIdHVjst1PtAVXPid1PDJ8yg8Ilj8cFWSBPP7eccp0GlwMqQXXUNPNDt bJOc+g6+XNxt7/NKQBPTuVjjOwmFO6KD9X3J8CacFsjq9Auo1clFm8M+8Hiv vqKy5Qq4/vFmq3fZAkxYtRvXLm2AyI0j3ZoxSuCa2yWYeZQBdRLVESY5UeDZ TrXmrjICGtDkUlLfQUfeBY+Za59hQSPfFqTvT3uJlKvANY3PRLQ9V0k4ArmN ZIq0mLJS2dGgis0EDyEVhOZV8aqgiRPVCjTx71LcUFvbvHVZwJaM++hzxAy+ UIMj3xQ+Pv7FjmsK8aKfDazgtkfNifNWbLhq1fahmbcB0DnFW62zzII7rOSv Nzalgr60opl7MBM+TMtPXdN4Bb3qQkw9awy43EaKTXPMR9g589hzlnkLu2im Q03MaAWPdxFcqV9XsbVZSmO683fgraZ8qsAXsOwPlpQUXzq0d+mdSH4zgzlZ p1AnXtGhxTFRKv1vOpZ1i7IB5v2QxiAYLX+mGSuEoLt+9u1g9srsoKheITAW W1NY4uvgWMHlz7083SBF4qxk7iqDYrzD5tzwGAgaxF/qF0iHOx5OMTP75yF7 20jh27sguO5g/vWE9DI88mYX9Ne1gSNYxRQPZR1CZG2P6o2rQ41byEigxA7k xBmYFWF7Yc8per8amYAmp6ADdyPmELlteeWAXGa0Pb/bA/GsQFQnaffCjhPR 0XrFjdOkIOQIIbjKPIuE8gWFUpy39JA8Z4oIkywnmiWWxrc1xY5QvqjcMJHh xPO7i6yOihnAGZK1xcJzEs5/fvIYz9Fb8Hy3iXm9BBHvbfB7Prw3GrgWuJy6 apjx6+ve5gnt2RDzNCZc+AQBFxalNJmeeQ+vm4d3ymzXsZpkNcGhF11wkvQk 67HqMnbz0GRO8/Eh2ByedFo2m8eu5Ud8vUgYhtry8Hz/e+OYkLEFlRQ4BEXc 12rqQ99hXenHOz1nmyE3o/J4jHITsOslhN43xcF18aCLWv8QuNG0iSwaBdBb VUmV4Z8Br8NKA3HacbDyfI+7yOsFCCLkmxpre0BLvVqaYuwqND8s+lnTcw58 9dvy+l5sArab+6ZU8FHYTpppuN/IgErMb9a8L2OGQ5WZL8fNmdDUKO7Ot2Ht iAr5kT95kQV9afpjTtoiDVGIeq++Yc2GhsW9CAxzvI4InORfKlpgR73FTzup jEoi3SHWp87bktE+dpe/txVn1JbqUT6uUjKu/9tTu1FNCQ7cm7EganLgOpI5 pV9DzMGBfOWVchEbTiNlpR3Q94V6u1SerJOsuEJ6rqPotSRQjU2L0O1mwhG/ KsNZ1WKoDXf5S1ybEZc7ss9iZqgaWgvZTb0LtjC0uOEAr/03UB9tyOFz+42J nRXXqD/dB0PlfPxHzBYxp9dmwXpAhwtX1i2uMM1iZUxWsTXf6aATNlyvVzqM mS06ZvJeGACJn32zcmyt2OUHWEF0ZAdE3nXclNGKA03u3LqY9AYI6hetkynq gNk54ye80u/A9qTAD4H4Ufjw8EwRS+JzKGy7d/z9zhzkHO9P3NJ5AF93jSar PFqCuPlCTRFNe0hKdV876LAG0d+F5NnPaYNckJtiWuQ2NEj0W1qS94GR7Xyu cTkj6t62pjo9uojcOnFZXOgCM7ovN9BA9zEN8UGY4otGWVF2QsZofF0o4npr 8CfRiITKy+qLMC0YIcJ2KqbS4xyoWICpskn3LoQ9mXRY248T1/12rzamRA+0 KnlXzVdJeNTEqc4D5i6Q9HK+Lf8OEfdkfObb2BsGDK4xNFkKC+7EPS2giGaC P2EDWwon4FU2jQF+vuUQctRwQINrAzN4Kln+3aYTuOR7QIC+jPHZsnhY+A9C Te9Cte3SPEaK5Xunu0QHvZOqzVotE5iehGFYCH0IQu2oL5OINEz4yJ+mlRzf 4IDNK2LzH3VwW6DnizJDNcjx7upuNRyE/p8oKp1VBNEIoW29aQpYWnIe3rFI gPO8ThvclAXAHsd/3KfuCQo3Pzkqra3AsOXpOGPiRZiWiKiYZtyEkO2PhdFl sqCYTnfb7cOAhs+Ly4kJsYN1f6nnJhsTqhBskDcr2Id46Va55KWxoE5HDS+V krORu2NbRsK8bOjDtHGPKX9XxLLE4+ClZ+yoyK4OL799sgg1IMo7YC8Z5cnb rbymuai2fSwrQ3IvGac4jrhW7lEHOeFASZmn7Pj+yrfkqQVrCOgXr7nFzYab KPxwsc8NglHHBKcfOSx4ho8RVSvlGVxu/HLwmQwTPpFtF/fO6zXkhBu680uu Yj1WeZvH7vWDYSPrDV3xBSw5Od95/z9/bGCQuqfNfhp7OlbhXeJFh+9eKc2B /r3AFD7jUZxfCusQNRh2bAI+5oYmejQ9gT2MPOxrdfNAkuvYJKUFAKG6nXCi bhmcrt9/3km3AnyYoZftzTqURBrdXg5GwOhaapTNxx3Qbj/WU5z4F/SKtP55 yIqAau//u45uNYGs0MinRzeY0W5dWc2CjlJkPcbfzc6XiM7/ej02PuaDTMZI hpX8JqFDkn5/uUloIAruY1Ndfpzo1oMzJ7UlmZA9jC6l18Y4cFVkVZvmaQzn LxTVhBiQ8PrY1qLRMg8o9CkfHe1jxUlNyu+Do2JBwD18j/cdZnzQMk61Ly8X 3PstOQSTljCvIOL0atIQ2HdWSbHd+4nNLklvhTENg4ZMf0iFwhjGeynjHA/P ENT2nnKN+XMYgub81dUP58IBNY9ae/sfED0pSYqPjoaEo7Qf0qaL4LAZF2s3 cBMc9r1pVzj8G653r0/aGhnCrpt7U5v0t8C94vEIVVgCaqOXhX/zMKJhvp9K WCwZ4EfSI3pLMRMacl+AWEJsRjZbnGJdNVnRy2dJYj1ySciykrdMVwkbKrwP 95Zjvop0t+A0Zi0ONMz1oGNglyhyLVKZfLiUjGa6UA75So6o/cfHDP/qP177 r/8PpIpxJw== "], {{{}, { EdgeForm[], Directive[{ Opacity[0.2], Hue[0.67, 0.6, 0.6]}], GraphicsGroup[{ Polygon[{{1, 179, 180, 25, 178, 95, 141, 49, 160, 73, 119, 24, 177, 94, 140, 48, 159, 72, 118, 23, 176, 93, 139, 47, 158, 71, 117, 22, 175, 92, 138, 46, 157, 70, 116, 21, 174, 91, 137, 45, 156, 69, 115, 20, 173, 90, 136, 44, 155, 68, 114, 19, 172, 89, 135, 43, 154, 67, 113, 18, 171, 88, 134, 42, 153, 66, 112, 17, 170, 87, 133, 41, 152, 65, 111, 16, 169, 86, 132, 40, 151, 64, 110, 15, 168, 85, 131, 39, 150, 63, 109, 14, 84, 130, 38, 62, 108, 13, 83, 129, 37, 61, 107, 12, 36, 60, 106, 11, 167, 82, 128, 35, 149, 59, 105, 10, 166, 81, 127, 34, 148, 58, 104, 9, 165, 80, 126, 33, 147, 57, 103, 8, 79, 125, 32, 56, 102, 7, 31, 55, 101, 6, 78, 124, 30, 146, 54, 100, 5, 164, 77, 123, 29, 145, 53, 99, 4, 163, 76, 122, 28, 144, 52, 98, 3, 162, 75, 121, 27, 143, 51, 97, 2, 161, 74, 120, 26, 142, 50, 96}}]}]}, {}, {}}, {{}, {}, { Hue[0.67, 0.6, 0.6], RGBColor[0, 0, 1], Line[{1, 96, 50, 142, 26, 120, 74, 161, 2, 97, 51, 143, 27, 121, 75, 162, 3, 98, 52, 144, 28, 122, 76, 163, 4, 99, 53, 145, 29, 123, 77, 164, 5, 100, 54, 146, 30, 124, 78, 6, 101, 55, 31, 7, 102, 56, 32, 125, 79, 8, 103, 57, 147, 33, 126, 80, 165, 9, 104, 58, 148, 34, 127, 81, 166, 10, 105, 59, 149, 35, 128, 82, 167, 11, 106, 60, 36, 12, 107, 61, 37, 129, 83, 13, 108, 62, 38, 130, 84, 14, 109, 63, 150, 39, 131, 85, 168, 15, 110, 64, 151, 40, 132, 86, 169, 16, 111, 65, 152, 41, 133, 87, 170, 17, 112, 66, 153, 42, 134, 88, 171, 18, 113, 67, 154, 43, 135, 89, 172, 19, 114, 68, 155, 44, 136, 90, 173, 20, 115, 69, 156, 45, 137, 91, 174, 21, 116, 70, 157, 46, 138, 92, 175, 22, 117, 71, 158, 47, 139, 93, 176, 23, 118, 72, 159, 48, 140, 94, 177, 24, 119, 73, 160, 49, 141, 95, 178, 25}]}}}], { AspectRatio -> GoldenRatio^(-1), Axes -> True, AxesLabel -> { Style["x", 24, Italic], Style[ Row[{"\[LeftBracketingBar]\[Psi](", Style["x", Italic], ")\!\(\*SuperscriptBox[\(\[LeftBracketingBar]\), \(2\)]\)"}], 24]}, AxesOrigin -> {-3.75, 0}, Method -> {"AxesInFront" -> True}, PlotRange -> {{-3.75, 3.75}, {0, 2.1}}, PlotRangeClipping -> True, PlotRangePadding -> { Scaled[0.02], Automatic}, Ticks -> {{-3, 0, 3}, {0, 1, 2}}, TicksStyle -> Directive[20, GrayLevel[0.5]]}], Attributes[PlotRange] = {ReadProtected}, $CellContext`psix[ Pattern[$CellContext`x, Blank[]], Pattern[$CellContext`k0, Blank[]], Pattern[$CellContext`x0, Blank[]], Pattern[$CellContext`a, Blank[]]] := ((1/(Pi^(1/4) Sqrt[$CellContext`a])) Exp[(I $CellContext`k0) $CellContext`x]) Exp[(-($CellContext`x - $CellContext`x0)^2)/( 2 $CellContext`a^2)], $CellContext`p2 = Graphics[{ Thickness[Large], RGBColor[0, 0, 1], Dashing[{Small, Small}], Line[{{-1., 0}, {-1., 2.}}]}], Attributes[Thick] = {ReadProtected}, $CellContext`p3a = Style[ Text[ Row[{"\[LeftAngleBracket]", OverHat[ Style["x", Italic]], "\[RightAngleBracket] = ", NumberForm[-1., {4, 2}]}]], RGBColor[0, 0, 1], 18], $CellContext`p3b = Style[ Text[ Row[{"\[CapitalDelta]", Style["x", Italic], " = ", NumberForm[0.7085209947489206, {4, 2}]}]], 18], $CellContext`p3 = Graphics[ Text[ Column[{ Style[ Text[ Row[{"\[LeftAngleBracket]", OverHat[ Style["x", Italic]], "\[RightAngleBracket] = ", NumberForm[-1., {4, 2}]}]], RGBColor[0, 0, 1], 18], Style[ Text[ Row[{"\[CapitalDelta]", Style["x", Italic], " = ", NumberForm[0.7085209947489206, {4, 2}]}]], 18]}], {2., 1.7}]], $CellContext`x2plot = Graphics[{ GraphicsComplex[CompressedData[" 1:eJw1lmk0lQsfxTmG4+C45+YWGaMkisosPP8nMnaUISVRlCFjChWuMVLmKWMD QqYMSYX0PIcypcg8ZDjmIZIx83vfte7da+211/66P+z1E7l6w8iGwMDA8Pof /z/n4rk6d3bIuLuD5PD9alngl09bvZnEgRcyCPLqO1+AK1nrEoJbbHjtY37R 0Q5PqBgTdGaMZMWFdPjS400eweEVEk3oMDPufLqq9ldtAZR2fhDziGfElTwH qBzaNMjk8lQgndvGMu5SjS8otMAfFFaNFJ41bIXaq7Uk3AsvSg7cfLK4iKlR M9TLl4agdzw3QMxgDhMpCC/tX6UDnidlvTQ1gk1z5PmbaQwC4XIu91n7duzE BCWU43UnJLkNGA8QEzBidvfO50+foYdrojpUqw1iFUsDya8qgL/66q0xzRGg 2la4rF3MhhvvpdH0t7MwJHSh8uPlcJCvdLRR3VyEgoPFAsrTzsB8V5qk8PE3 FLZybNuUUiE7/kpY1eIWmEilJIgt74eIBzse9jaM6KWhtpKzrWtIye37uyuZ mVH7bLvmFLM65EP8qcy2RFY0nljrnNgdg7weVhYt3WZDZbxTRF0CzZB4S9uo i8kcaKlUUSzRkA/5d390ZJNIc53uVWO26RpXauLEeVwHM1BGLVBz/hJdp8eO t3JF+9Wr20O4ZvjpqE9EXCFvo8SY9QEszHLzRJuz4PLfVDKqptLhhq31YsMg Adf7++si28gbIBT5DKleYcAT50beXFWoB7Mo7P23sg2sJ2Qla0K0A/osd/em Bq9gCw73z0qFDkBo6yZvd8QvjFrW0OXZQ4cv9TMLnIJTWGTQr8iXcnSgXSTM pQoNYIdHVjst1PtAVXPid1PDJ8yg8Ilj8cFWSBPP7eccp0GlwMqQXXUNPNDt bJOc+g6+XNxt7/NKQBPTuVjjOwmFO6KD9X3J8CacFsjq9Auo1clFm8M+8Hiv vqKy5Qq4/vFmq3fZAkxYtRvXLm2AyI0j3ZoxSuCa2yWYeZQBdRLVESY5UeDZ TrXmrjICGtDkUlLfQUfeBY+Za59hQSPfFqTvT3uJlKvANY3PRLQ9V0k4ArmN ZIq0mLJS2dGgis0EDyEVhOZV8aqgiRPVCjTx71LcUFvbvHVZwJaM++hzxAy+ UIMj3xQ+Pv7FjmsK8aKfDazgtkfNifNWbLhq1fahmbcB0DnFW62zzII7rOSv Nzalgr60opl7MBM+TMtPXdN4Bb3qQkw9awy43EaKTXPMR9g589hzlnkLu2im Q03MaAWPdxFcqV9XsbVZSmO683fgraZ8qsAXsOwPlpQUXzq0d+mdSH4zgzlZ p1AnXtGhxTFRKv1vOpZ1i7IB5v2QxiAYLX+mGSuEoLt+9u1g9srsoKheITAW W1NY4uvgWMHlz7083SBF4qxk7iqDYrzD5tzwGAgaxF/qF0iHOx5OMTP75yF7 20jh27sguO5g/vWE9DI88mYX9Ne1gSNYxRQPZR1CZG2P6o2rQ41byEigxA7k xBmYFWF7Yc8per8amYAmp6ADdyPmELlteeWAXGa0Pb/bA/GsQFQnaffCjhPR 0XrFjdOkIOQIIbjKPIuE8gWFUpy39JA8Z4oIkywnmiWWxrc1xY5QvqjcMJHh xPO7i6yOihnAGZK1xcJzEs5/fvIYz9Fb8Hy3iXm9BBHvbfB7Prw3GrgWuJy6 apjx6+ve5gnt2RDzNCZc+AQBFxalNJmeeQ+vm4d3ymzXsZpkNcGhF11wkvQk 67HqMnbz0GRO8/Eh2ByedFo2m8eu5Ud8vUgYhtry8Hz/e+OYkLEFlRQ4BEXc 12rqQ99hXenHOz1nmyE3o/J4jHITsOslhN43xcF18aCLWv8QuNG0iSwaBdBb VUmV4Z8Br8NKA3HacbDyfI+7yOsFCCLkmxpre0BLvVqaYuwqND8s+lnTcw58 9dvy+l5sArab+6ZU8FHYTpppuN/IgErMb9a8L2OGQ5WZL8fNmdDUKO7Ot2Ht iAr5kT95kQV9afpjTtoiDVGIeq++Yc2GhsW9CAxzvI4InORfKlpgR73FTzup jEoi3SHWp87bktE+dpe/txVn1JbqUT6uUjKu/9tTu1FNCQ7cm7EganLgOpI5 pV9DzMGBfOWVchEbTiNlpR3Q94V6u1SerJOsuEJ6rqPotSRQjU2L0O1mwhG/ KsNZ1WKoDXf5S1ybEZc7ss9iZqgaWgvZTb0LtjC0uOEAr/03UB9tyOFz+42J nRXXqD/dB0PlfPxHzBYxp9dmwXpAhwtX1i2uMM1iZUxWsTXf6aATNlyvVzqM mS06ZvJeGACJn32zcmyt2OUHWEF0ZAdE3nXclNGKA03u3LqY9AYI6hetkynq gNk54ye80u/A9qTAD4H4Ufjw8EwRS+JzKGy7d/z9zhzkHO9P3NJ5AF93jSar PFqCuPlCTRFNe0hKdV876LAG0d+F5NnPaYNckJtiWuQ2NEj0W1qS94GR7Xyu cTkj6t62pjo9uojcOnFZXOgCM7ovN9BA9zEN8UGY4otGWVF2QsZofF0o4npr 8CfRiITKy+qLMC0YIcJ2KqbS4xyoWICpskn3LoQ9mXRY248T1/12rzamRA+0 KnlXzVdJeNTEqc4D5i6Q9HK+Lf8OEfdkfObb2BsGDK4xNFkKC+7EPS2giGaC P2EDWwon4FU2jQF+vuUQctRwQINrAzN4Kln+3aYTuOR7QIC+jPHZsnhY+A9C Te9Cte3SPEaK5Xunu0QHvZOqzVotE5iehGFYCH0IQu2oL5OINEz4yJ+mlRzf 4IDNK2LzH3VwW6DnizJDNcjx7upuNRyE/p8oKp1VBNEIoW29aQpYWnIe3rFI gPO8ThvclAXAHsd/3KfuCQo3Pzkqra3AsOXpOGPiRZiWiKiYZtyEkO2PhdFl sqCYTnfb7cOAhs+Ly4kJsYN1f6nnJhsTqhBskDcr2Id46Va55KWxoE5HDS+V krORu2NbRsK8bOjDtHGPKX9XxLLE4+ClZ+yoyK4OL799sgg1IMo7YC8Z5cnb rbymuai2fSwrQ3IvGac4jrhW7lEHOeFASZmn7Pj+yrfkqQVrCOgXr7nFzYab KPxwsc8NglHHBKcfOSx4ho8RVSvlGVxu/HLwmQwTPpFtF/fO6zXkhBu680uu Yj1WeZvH7vWDYSPrDV3xBSw5Od95/z9/bGCQuqfNfhp7OlbhXeJFh+9eKc2B /r3AFD7jUZxfCusQNRh2bAI+5oYmejQ9gT2MPOxrdfNAkuvYJKUFAKG6nXCi bhmcrt9/3km3AnyYoZftzTqURBrdXg5GwOhaapTNxx3Qbj/WU5z4F/SKtP55 yIqAau//u45uNYGs0MinRzeY0W5dWc2CjlJkPcbfzc6XiM7/ej02PuaDTMZI hpX8JqFDkn5/uUloIAruY1Ndfpzo1oMzJ7UlmZA9jC6l18Y4cFVkVZvmaQzn LxTVhBiQ8PrY1qLRMg8o9CkfHe1jxUlNyu+Do2JBwD18j/cdZnzQMk61Ly8X 3PstOQSTljCvIOL0atIQ2HdWSbHd+4nNLklvhTENg4ZMf0iFwhjGeynjHA/P ENT2nnKN+XMYgub81dUP58IBNY9ae/sfED0pSYqPjoaEo7Qf0qaL4LAZF2s3 cBMc9r1pVzj8G653r0/aGhnCrpt7U5v0t8C94vEIVVgCaqOXhX/zMKJhvp9K WCwZ4EfSI3pLMRMacl+AWEJsRjZbnGJdNVnRy2dJYj1ySciykrdMVwkbKrwP 95Zjvop0t+A0Zi0ONMz1oGNglyhyLVKZfLiUjGa6UA75So6o/cfHDP/qP177 r/8PpIpxJw== "], {{{}, { EdgeForm[], Directive[{ Opacity[0.2], Hue[0.67, 0.6, 0.6]}], GraphicsGroup[{ Polygon[{{1, 179, 180, 25, 178, 95, 141, 49, 160, 73, 119, 24, 177, 94, 140, 48, 159, 72, 118, 23, 176, 93, 139, 47, 158, 71, 117, 22, 175, 92, 138, 46, 157, 70, 116, 21, 174, 91, 137, 45, 156, 69, 115, 20, 173, 90, 136, 44, 155, 68, 114, 19, 172, 89, 135, 43, 154, 67, 113, 18, 171, 88, 134, 42, 153, 66, 112, 17, 170, 87, 133, 41, 152, 65, 111, 16, 169, 86, 132, 40, 151, 64, 110, 15, 168, 85, 131, 39, 150, 63, 109, 14, 84, 130, 38, 62, 108, 13, 83, 129, 37, 61, 107, 12, 36, 60, 106, 11, 167, 82, 128, 35, 149, 59, 105, 10, 166, 81, 127, 34, 148, 58, 104, 9, 165, 80, 126, 33, 147, 57, 103, 8, 79, 125, 32, 56, 102, 7, 31, 55, 101, 6, 78, 124, 30, 146, 54, 100, 5, 164, 77, 123, 29, 145, 53, 99, 4, 163, 76, 122, 28, 144, 52, 98, 3, 162, 75, 121, 27, 143, 51, 97, 2, 161, 74, 120, 26, 142, 50, 96}}]}]}, {}, {}}, {{}, {}, { Hue[0.67, 0.6, 0.6], RGBColor[0, 0, 1], Line[{1, 96, 50, 142, 26, 120, 74, 161, 2, 97, 51, 143, 27, 121, 75, 162, 3, 98, 52, 144, 28, 122, 76, 163, 4, 99, 53, 145, 29, 123, 77, 164, 5, 100, 54, 146, 30, 124, 78, 6, 101, 55, 31, 7, 102, 56, 32, 125, 79, 8, 103, 57, 147, 33, 126, 80, 165, 9, 104, 58, 148, 34, 127, 81, 166, 10, 105, 59, 149, 35, 128, 82, 167, 11, 106, 60, 36, 12, 107, 61, 37, 129, 83, 13, 108, 62, 38, 130, 84, 14, 109, 63, 150, 39, 131, 85, 168, 15, 110, 64, 151, 40, 132, 86, 169, 16, 111, 65, 152, 41, 133, 87, 170, 17, 112, 66, 153, 42, 134, 88, 171, 18, 113, 67, 154, 43, 135, 89, 172, 19, 114, 68, 155, 44, 136, 90, 173, 20, 115, 69, 156, 45, 137, 91, 174, 21, 116, 70, 157, 46, 138, 92, 175, 22, 117, 71, 158, 47, 139, 93, 176, 23, 118, 72, 159, 48, 140, 94, 177, 24, 119, 73, 160, 49, 141, 95, 178, 25}]}}}], { Thickness[Large], RGBColor[0, 0, 1], Dashing[{Small, Small}], Line[{{-1., 0}, {-1., 2.}}]}, Text[ Column[{ Style[ Text[ Row[{"\[LeftAngleBracket]", OverHat[ Style["x", Italic]], "\[RightAngleBracket] = ", NumberForm[-1., {4, 2}]}]], RGBColor[0, 0, 1], 18], Style[ Text[ Row[{"\[CapitalDelta]", Style["x", Italic], " = ", NumberForm[0.7085209947489206, {4, 2}]}]], 18]}], {2., 1.7}]}, {AspectRatio -> GoldenRatio^(-1), Axes -> True, AxesLabel -> { Style["x", 24, Italic], Style[ Row[{"\[LeftBracketingBar]\[Psi](", Style["x", Italic], ")\!\(\*SuperscriptBox[\(\[LeftBracketingBar]\), \(2\)]\)"}], 24]}, AxesOrigin -> {-3.75, 0}, Method -> {"AxesInFront" -> True}, PlotRange -> {{-3.75, 3.75}, {0, 2.1}}, PlotRangeClipping -> True, PlotRangePadding -> { Scaled[0.02], Automatic}, Ticks -> {{-3, 0, 3}, {0, 1, 2}}, TicksStyle -> Directive[20, GrayLevel[0.5]]}], $CellContext`xplot = Graphics[ GraphicsComplex[CompressedData[" 1:eJx12Wk8VwkXwHE7f2JMpqgs0UqlTaS456akpJI2idIUJUsqmmQSUhqUtbLU hFJZImklcy8KlVLImp0kaWTN/jzP5/Ocl8cLPt+3+N97zu+o/37Ewk5ESEjo t/9++9/P7xFy5ePjsrzbYa2m87lLYdqy2IGjkTJ8qpCK0kbnnbA3YUhTZVSK z782TaPlowdktqo4C1+S4FXXTY2L2H4Z5vULclTnifHOG7Lzf+SnQEb5P7Pc I4T55R51ZjImOXBLzkNXsG2Miz9ptnWn7nv4RV5idbTiINdvVr22V60a7qTP PHq9p4czNIs3etbbANWfE31mmX/n1FOCMmoHGoFPWnCgt72Z+yqT5G21uh5E 9iQqbHYo41a0yQfIPCyHyON1W+skr3CStyvH37x8A1VybbkBa0shTC/DV/ZB JkzL/f1Yq3EzmNlnugzuug1HnmuzcU86oUF1Z9aLPUGwLMvRzmCkB1Jm31fW /+oMYie1BbovfkJqicyYXYYZ3I7YG5jdMwrbF0RfmdU3Ay5eGHd3sBNmdzeU pm8uGWTST5yflCUmxjrcPlgcbVXA/BOx5lbpVQk2QjLf+WplKPOwSV8jY0yK XeIZreHia8VE2NoH74qSYTMWpIVJbpnK/P/3zzaPSOa4fq02FLOr+Ly8aAKv 6FofzwqvBUPntyEFptJ8iVzImUIjBwgyDtoQ/FKS100aTt8qcQG6OxUUQ6zF +WUfVsZnt8fBEfsDPa/qRXjTP9/1SDU/BpG00w0Ge4X4q9+bH/+uWwhWwdzz D4+GuSr//oQ2jY9QYzupOuZcP9d9+PzmBQF1EFAyolR58Qdn9uhVhUdVI7wt 7OieoNLOXfL7cemeTiPk7BL5HqNax81rHii3MaoBA+O2n0WvXnLmqdcd788u gdg5ibUTPudAlnJ/w8HcPLiwvrxUq/0TeMkplD5PSgdjbt2uPK8vkDquUV9Y EwWPg3J8JZx+gFluVNpI02m4NmWjnr5tP7j+8ni0us8GtkuYvB7cPQzqR+ZX GocuB9fECpVbC4VYJ411agInebgxnms88ZEI61Pkkl74sZF5eq7V2mSTOHvp SUrcjNh7zLOVsH/1G0m2LHG52kXmBHNL/b2lhJk065c5csVddSWTcyrzQUrR BHat73bvCr1hw8GRY3uU7WX50xtlQuvvGML8D7ovrv2Q5o1Vldg35vvghHve ih37pHiD7LG5HU98oLxdKXddnzh/uD956HVRDGzU1rNyOyfKN+UkxwyufgDV RqqiVYNCvM5wtF1x6AsY33TNo1NslNtltc7sanwJuD+9KBfzboAb7JR/Hef8 CZRy5V9m8t3c7X9s5aO9GqGswnRF1OMOzulAtFnbg0Z473h1QdyfjVzCMflh sK6FWCGVkGWbirlU8Dt5xqEMrB5YzdYwTQXh+wfkxSMKYFHKnjfVipWwQDAh S6ziEdznP9pta2oFFfOI3bXKcfCHu1Nox4wuuD1mofvhqR8cOmz9boV2H1z2 lFbxXm8H87nMdkX5IfBfar/Q9LMR5B33b/bVHIe74eZWadwUmLymsdZQVoSN imbrTl78zuiMLdP3SRRjy5Ir3RmPTMbgS87ZwMWSbEuh3vAGgR8zX+RctnWC gJ3qFyDvPGrKJDnLq4suncAmzIqdOtouzci/XXlk+5IJfHJl2r6Fs8xhk+CA TfdNAT9tx5dFiguPwc1J260LNSX56ldnbjZNCQG5bjmnijwx/tCQp/WVstsQ +ndokNoKEV5NQ77IctNzeFjcNP7IfojLizJUabhTAasE1xOuGfRxR+d+uVu8 uAFGmr449Vl1cfuTL77bJdIE+c+Ckr3PfuZUt9qYCXwbIE1hf15hwFOuIm5x uUdnMSTGZy0O1S8CadMrAecteXDtme1iWNsAx3NMJMVXp0B1dpbZkmkdcGre 8rpwk3DovznZTf1hN/iJJFtuNXGH94WGsXphA1D8V9q/eVXbwGtjaVLNnRHg JikcXXBuIYxFdrw6/1qI1ewayXv+SAzmZt2699lalI0JVih/EljGrJS97C3b I87es/z2XdsmltENfm40fECKDQy/4xvoeIhRXjWtN61bmvWcs8FpZYsWU+l/ YM0Oe1m2RtrlzzG9DsPeQnaqXIYsv/Gnh8lrw+Uw82yHjaSxDL9O627GO39r OCy794F+mhSfI0iInbnRCwoPxigmrJLgdeMSHTX2R4JBWOzF9ZWiPHMme0un wX3ID3L5bY6JMK8zf7pNR0MulKRKW3qmjHLs/VczlRw+gFHLq7tTj//kZm2e s7pwQw00PJs6bb5VD+f00OqcKTTCzr1DNntFO7lHovvC8j41wrrApkLTjCbO qsfxltLOOtD8t6ZTR6qE23OBSwm59BEunXQcWbI2HIwVEgtC416BX61GwZK0 j9D5fet1Je2nYL9K+ZtyRAv889emNPGrNyG19Ozi5+Pf4e7i2quj6y7Au4kt USsv90J4V6qxurEDRMa4Dc4+PAghn1SXSW8zAR2/43qxl8bglWatra3sdLCw 70rc+kyYdSsdNPja0sMcW7FnjupOMXZ6oq/5+ms5zGlGNCKtRYKVFolviSgI YFyP1f8raSFgly3dqC7abcGoHVxpqf1Zhp3lY6m/vXIiIx0lmGdyZgK//sPZ /NB0U1ibpTRgPSDgg9vWlM+0doHIe12lyX9I8h7CN7xeVweCkGtozlJ5cd5J 4auyHnsLvEWGud4gET7b7rXPGa9n4L9wS91quWHO/G+tZ5/sykFuWRUoN/Zx U+3F3W286yGvujvXvreLE4RNfbq+txFMVxkUr33fxplqbgn0b2yAgINm9yIl czi1+b9aZsl8gJl2DySLfymAE8pVb/WFckFHaWJlyZZ6qP2XZbUT0iCEESkd KmoH8fd3//rD5grsUHIaVpDvBu5axIvpRh6ge/Sl4/LBfmiy3RC+VXIXfNW8 mPlVeAT8x16khjxaCnpxjccnnRZig7rm6MxSlYYDtRkeI1KirO4586ROlRrm 1Ppsl6RYcdZp4ZbdGbK3mZOtoxZqSlLsX7Gf3du9XRnbdPfZu29Is+oTP546 M30pY+YT7OkzRZZVTJqkP2jcYzi2KCFea4osL+/Y7Jo12Qh01Hy1lvwtzc/I eiLb3n0AfGrn5B1TkOK3635zcUj0gxbHK07f7orz8actzNZG34A9r9/OvrFE lG+7fTD86amHcDdoi9s0rQGual/SyKKztbDltcSR9XO6uaioZOcZ/30em5vH TC51+Mr93ZrpmX6qET6dii729a4G0aAO9/vJGTAEwfWBi9rgRWLAVfei6zBZ WFF6sKALBDofRwSxPiCSWyayoqAPnA6dv1neuA/4JqFqqcdDkH7J4kTfOQYs 9scE270YB5OyRVX3r/4G1eolv87dJ8KazPizoHFfG9OfI7uhZViMrVy/1Djl YwYzFOp9/KCXJNv142Hr59bTzJdQrcD0nwK2QevMb8c1VzO6bq3tFWcmsKMX Nq0y0RJlJgu7ZOxvleENmAGTHI+tsGNnWp6/uYAvDCtJa3nkDqmnn7W01Ejw giL95+eCw0DZLWiy5x9ifL1tuEFNUiK41drKqET2cqf8JL8ORDaAQ3n2Aqmz /3KdvdqjgaJNsHpJrX+mbiuntDt+m6JiA+RXr3EN/bUJ/L57GxnNS4SZhu75 Dg7fIOSLliAiJASuLMz5pm3ZA4dHwsMO1h2Fw9Mfl+nO+wmHKoe+2FtsgYlH p8QUbRwFt8xrzWZqmpAf0qf2U1GYDfR6mS5uKwTfIi83vr8vyvqfV5ZMlyxm Rt47hbkaS7B7NgtmVelEMn3LPZdUpEuxatN5Tx2x35nK93yO2FoZNtB1tqNv hQaz/5K+7LwMWfaWi/xcL61mQ5yPhf7/hc9Pyjg/UMb/T8o4/1HG5wdlfH9S xr83ZZz/KeP7gjLOS5Tx80gZ513K+LykjPMCZfz/poz7DmV8P1LG+ZAyPn8o 43xPGd8PlHE+ooyfZ8q431HGeYAyzsOU8XlLGfcZyvg+pIzzIGV8flHGfZYy zj+Ucf6njO8Xyri/Ucb3P2Wcfynjfk4Z5znKuM9Qxn2TMvYAyjg/Usb9iTLu t5RxXqKM+wJl7BeUcd6ljPseZZw3KOO+ThnnP8q4/1DG9zll7DWUcb6njPst ZZyvKGOfoIzzLmXc9yjj/EIZ+xRl3Gco4z5PGedJythjKON8Txn3W8o4r1HG HkcZ9zfK2C8oY1+ijP2PMu6LlLGXUMaeRRn3JcrYCyhjr6SM+y1l7DuUsb9R xv2OMvYNythXKeM+Thl7FGXcnyhjT6SM+ypl7DWUcT+hjD2ZMvYHytjfKOO+ SBn7KWXczyljn6KM+xhl7OeUsbdQxt5IGfdjytiLKWOPoIw9jjLun5TxXkAZ +xJl7KuUsQdQxj5OGfsLZeyPlHHfpoz3EcrY0yhjT6aM/YMy3gMoY2+ijL2V MvYFyngPooz9kDL2c8rYeyjj/YMy9jXK2JcpY0+hjPcvythLKeO9gDL2Lcp4 76GMPZEy9nTK2I8o472PMvZhyngfoYw9jzLetyhjP6WM9wPK2Mso432TMvZw yngPooz9kjLe8yhjL6aM9xLK2Acp4z2XMvZ/ynj/ooy9ljLeLyljH6eM9yHK 2EMp4/2aMt47KOO9jzL2acp4r6WM9wDKeA+jjP2XMt7r0f8BXU3VQA== "], {{{ EdgeForm[], GrayLevel[0.5], GraphicsGroup[{ Polygon[CompressedData[" 1:eJwt1nWwVVUUgPG1LvDofLSET0REukVaRBoFpKVDUekuURGQLlEBUVJFRKS7 u7u7u7v91qz9x2/mm7P33WefmrkxzdrVaBsRkTmIDcU8zEeTYAEWIj9s7jqs R1MMxxIsRfpgGZaje7ACK1EprLEIi8NvJ2MN1oa1bc4qrA5jI3EER5EhOIbj 6IkR2IKteC3Yhu3ogQLYhM1hbmXswm5MCfZgL2IF+7AfzcI1bsDGsFZBHMLh sDebcwAHw5idcwd2hnPZHk/gJKpgNJ7gKTJhKs7gbLj/VXELtzENzXEBF1Eo uITLGBVcwVVkDGucw/nw2164gZthbZtzDdfDWBHE4aFHIXPY4ymcDntrgQd4 iMLBIzwO1xIH93A/zLVreobn6B28wEtUC17BXrSocI13cDes1dKeAWOx1fdm c5SOqI/ZHuPS8RBXXHw6AVqJS0gnwrv060hKJ0Mf8WOJ6STqY2PsnaEzIEZ8 TnI6BT4SF02ntHOKz8lIZ8LX9GdIQ6dFUfE5qejU6mN2LB2dXv1c9pvMdm58 TL+BXHRu9KWnIwv9JuLT7yE7/Q5+pD9HNvpt9TE7loPOqb7Wd2hKN8Mn4ueI sTH1te0ceei8qC4uH50ff4grQBe0eyquEF0YrcUVsXuLYvRYFKOLIwtdHBXp SnYN9DcoRZdGDXFl6Pfxp7iy9AdIKL5GCbqk+m+/QHm6gvraNqcc/aH6mO2h qN0L9b3YOSvTVewdoL+0Z2j3GiXEj1Wlq6mP2bHqtjdkFVfT7h2+pd9CY7qJ +r21Y7Xo2qhp7xLq0fXxlfixOnRd9bGSaEg3Ul/L5jSgP1Ufs2ec1cbUn609 s+Z0C3tH6c44RB+2a6bb2Dtnc1HK3m10obuiLf2TXbPtBdnEtbEx9BPXjm6P WuJrtLZ7qf7bv9CJ7qy+ts3pQHdUH/sFQ+ihyC5uGD0c/emf0Yvube+ouD72 reB7ujR60D3V59a2e2r3FjPE9bO59s2K608PQDvxa+xGd1dfqwwG0YPV92Zz BtI/qI/ZOfvau6R+LtvjCHok6tDjMZP+BznovzHGvjUkp+tiMj0FM+n2do12 LnuHxY2jx2OcuAn0r/bNiq8x1u6t+m8H4Hd6kvraNmci/Zv6WEcsohfbNyG+ x1H0aPW9dbBvxp4FyoqbYWPq15IC0+1bVp9r1zSL/hcDxc2m/0M9cXPouXYP xK9xKj1Nfa1oLKAXqu/N5syj56uP2R6X0EsxQdwyejlyiltBr7RnQtfHGnot ZokfW0WvVh/LhR30TgwSn7OOXo+U4jbQG9FJfM4uejca0OWwhd5qz0B8ziZ6 s/qYHdtGb1c/l/1mD73X7hE9GKfo0/aN0qlwgD6o/i1OxDH6OHKLf5NH6KPq Y3bsBH1SfS37hlvSrdS/XTvHPnq/+tp2jjP0WcwWd44+j9TiLtAX0UXcJfoy you7Ql+1d4jOgxv0TQyxdw3P6OfISzfEHfquvQPi7tH3kUbcA/ohuoqvcYu+ rf7bCnhCP1Vf2+Y8oh+rj9kertHX1fdi53xBv8RQuhGUP3qRiP/ntGOvGLM/ fzZmx2LRsZFWXBw6Ct3oxvZN0SkwV/xYXDoeKtKTkJBOhHzix+LTCSI+NgxJ 6WQRX8vmJKaTRHzM1oymUyId/T+XEkGW "]]}]}}, {{}, {}, { Hue[0.67, 0.6, 0.6], RGBColor[0, 0, 1], Line[{1, 96, 50, 142, 26, 120, 74, 161, 2, 97, 51, 143, 27, 121, 75, 162, 3, 98, 52, 144, 28, 122, 76, 163, 4, 99, 53, 145, 29, 123, 77, 164, 5, 100, 54, 146, 30, 124, 78, 6, 101, 55, 31, 7, 102, 56, 32, 125, 79, 8, 103, 57, 147, 33, 126, 80, 165, 9, 104, 58, 148, 34, 127, 81, 166, 10, 105, 59, 149, 35, 128, 82, 167, 11, 106, 60, 36, 12, 107, 61, 37, 129, 83, 13, 108, 62, 38, 130, 84, 14, 109, 63, 150, 39, 131, 85, 168, 15, 110, 64, 151, 40, 132, 86, 169, 16, 111, 65, 152, 41, 133, 87, 170, 17, 112, 66, 153, 42, 134, 88, 171, 18, 113, 67, 154, 43, 135, 89, 172, 19, 114, 68, 155, 44, 136, 90, 173, 20, 115, 69, 156, 45, 137, 91, 174, 21, 116, 70, 157, 46, 138, 92, 175, 22, 117, 71, 158, 47, 139, 93, 176, 23, 118, 72, 159, 48, 140, 94, 177, 24, 119, 73, 160, 49, 141, 95, 178, 25}, VertexColors -> Automatic]}}}, VertexColors -> { Hue[-0.3873239474347511], Hue[-0.19597924091782545`], Hue[0.011460347311615294`], Hue[0.20515326542384069`], Hue[0.39504669736209447`], Hue[-0.3989649889871367], Hue[-0.2067233454535833], Hue[0.0016131797924853512`], Hue[0.20615021886458226`], Hue[0.39694058781946384`], Hue[-0.3961741615131395], Hue[-0.20303558096295804`], Hue[-0.013696486586748354`], Hue[0.19173748950197642`], Hue[0.38342479547348596`], Hue[-0.4087930168424895], Hue[-0.20481031533243646`], Hue[-0.014574283939598892`], Hue[0.19175662916575387`], Hue[0.3843408721538913], Hue[-0.40698000314545607`], Hue[-0.20210036461877523`], Hue[-0.010967396209309739`], Hue[0.19626045391267108`], Hue[0.3873239474347511], Hue[-0.29165159417628816`], Hue[-0.09225944680310508], Hue[0.1083068063677281], Hue[0.30009998139296773`], Hue[0.49804085418747884`], Hue[-0.3028441672203599], Hue[-0.10255508283054904`], Hue[0.1038816993285338], Hue[0.30154540334202307`], Hue[-0.49961678684683786`], Hue[-0.29960487123804874`], Hue[-0.1083660337748532], Hue[0.08902050145761405], Hue[0.2875811424877312], Hue[0.4873158893154983], Hue[-0.306801666087463], Hue[-0.10969229963601777`], Hue[0.08859117261307749], Hue[0.28804875065982255`], Hue[0.4886804345042176], Hue[-0.30454018388211557`], Hue[-0.10653388041404252`], Hue[0.09264652885168066], Hue[0.2917922006737111], Hue[-0.3394877708055196], Hue[-0.14411934386046527`], Hue[0.05988357683967158], Hue[0.2526266234084042], Hue[0.44654377577478666`], Hue[-0.35090457810374825`], Hue[-0.1546392141420662], Hue[0.052747439560509576`], Hue[0.25384781110330273`], Hue[0.448661900486313], Hue[-0.3478895163755941], Hue[-0.1557008073689056], Hue[0.03766200743543284], Hue[0.2396593159948538], Hue[0.4353703423944921], Hue[-0.35779734146497616`], Hue[-0.1572513074842272], Hue[0.03700844433673922], Hue[0.2399026899127882], Hue[0.4365106533290544], Hue[-0.3557600935137859], Hue[-0.15431712251640872`], Hue[0.04083956632118546], Hue[0.24402632729319096`], Hue[-0.24381541754705693`], Hue[-0.040399549745744875`], Hue[0.15673003589578438`], Hue[0.3475733393775312], Hue[-0.45046206739982897`], Hue[-0.05047095151903178], Hue[0.15501595909655805`], Hue[0.3492429955807434], Hue[-0.44789547417998865`], Hue[-0.06103126018080077], Hue[0.14037899547979524`], Hue[0.3355029689806086], Hue[-0.46073856376349565`], Hue[-0.25580599070994964`], Hue[-0.062133291787808326`], Hue[0.14017390088941575`], Hue[0.3361948114068568], Hue[-0.45914978432061926`], Hue[-0.25332027425044534`], Hue[-0.05875063831167625], Hue[0.1444534913821759], Hue[0.3395580740542313], Hue[-0.3634058591201355], Hue[-0.17004929238914548`], Hue[0.035671962075643576`], Hue[0.22888994441612243`], Hue[0.42079523656844053`], Hue[-0.3749347835454424], Hue[-0.1806812797978248], Hue[0.027180309676497462`], Hue[0.22999901498394243`], Hue[0.42280124415288844`], Hue[-0.3720318389443668], Hue[-0.17936819416593183`], Hue[0.011982760424342244`], Hue[0.2156984027484151], Hue[0.40939756893398904`], Hue[-0.3832951791537329], Hue[-0.18103081140833188`], Hue[0.011217080198570163`], Hue[0.21582965953927097`], Hue[0.41042576274147297`], Hue[-0.3813700483296211], Hue[-0.17820874356759198`], Hue[0.014936085055937862`], Hue[0.22014339060293103`], Hue[-0.26773350586167255`], Hue[-0.06632949827442512], Hue[0.13251842113175613`], Hue[0.32383666038524944`], Hue[-0.47621060660617504`], Hue[-0.0765130171747904], Hue[0.1294488292125459], Hue[0.32539419946138326`], Hue[-0.4737561305134133], Hue[-0.08469864697782699], Hue[0.11469974846870462`], Hue[0.3115420557341699], Hue[-0.48671133722399873`], Hue[-0.2813038283987063], Hue[-0.08591279571191303], Hue[0.11438253675124668`], Hue[0.31212178103333965`], Hue[-0.4852346749082007], Hue[-0.2789302290662803], Hue[-0.08264225936285922], Hue[0.11855001011692824`], Hue[0.31567513736397107`], Hue[-0.3155696824909038], Hue[-0.11818939533178503`], Hue[0.08409519160369985], Hue[0.27636330240068596`], Hue[0.4722923149811328], Hue[0.0783145694445217], Hue[0.2776966072226629], Hue[0.47452255681973765`], Hue[0.26362022924129247`], Hue[0.46134311585499516`], Hue[-0.33229950377621964`], Hue[-0.13347180356012248`], Hue[0.06279980847490828], Hue[0.26397572028630545`], Hue[0.46259554391663593`], Hue[-0.33015013869795073`], Hue[-0.13042550146522575`], Hue[0.06674304758643305], Hue[0.26790926398345116`], Hue[-0.21989732923244132`], Hue[-0.014469601217064657`], Hue[0.1809416506598127], Hue[0.371310018369813], Hue[0.18058308898057016`], Hue[0.37309179170010354`], Hue[-0.42203481784656405`], Hue[0.3594638822270473], Hue[-0.4347657903029926], Hue[-0.23030815302119298`], Hue[-0.0383537878637036], Hue[0.1659652650275848], Hue[0.36026784178037413`], Hue[-0.4330648937330378], Hue[-0.22771031943461043`], Hue[-0.034859017260492994`], Hue[0.17035697264742347`], Hue[0.3634410107444912], Hue[-0.3873239474347511], Hue[-0.3634058591201355], Hue[-0.3634058591201355], Hue[-0.3394877708055196], Hue[-0.3394877708055196], Hue[-0.3155696824909038], Hue[-0.3155696824909038], Hue[-0.29165159417628816`], Hue[-0.29165159417628816`], Hue[-0.26773350586167255`], Hue[-0.26773350586167255`], Hue[-0.24381541754705693`], Hue[-0.24381541754705693`], Hue[-0.21989732923244132`], Hue[-0.21989732923244132`], Hue[-0.19597924091782545`], Hue[-0.19597924091782545`], Hue[-0.17004929238914548`], Hue[-0.17004929238914548`], Hue[-0.14411934386046527`], Hue[-0.14411934386046527`], Hue[-0.11818939533178503`], Hue[-0.11818939533178503`], Hue[-0.09225944680310508], Hue[-0.09225944680310508], Hue[-0.06632949827442512], Hue[-0.06632949827442512], Hue[-0.040399549745744875`], Hue[-0.040399549745744875`], Hue[-0.014469601217064657`], Hue[-0.014469601217064657`], Hue[0.011460347311615294`], Hue[0.011460347311615294`], Hue[0.035671962075643576`], Hue[0.035671962075643576`], Hue[0.05988357683967158], Hue[0.05988357683967158], Hue[0.08409519160369985], Hue[0.08409519160369985], Hue[0.1083068063677281], Hue[0.1083068063677281], Hue[0.13251842113175613`], Hue[0.13251842113175613`], Hue[0.15673003589578438`], Hue[0.15673003589578438`], Hue[0.1809416506598127], Hue[0.1809416506598127], Hue[0.20515326542384069`], Hue[0.20515326542384069`], Hue[0.22888994441612243`], Hue[0.22888994441612243`], Hue[0.2526266234084042], Hue[0.2526266234084042], Hue[0.27636330240068596`], Hue[0.27636330240068596`], Hue[0.30009998139296773`], Hue[0.30009998139296773`], Hue[0.32383666038524944`], Hue[0.32383666038524944`], Hue[0.3475733393775312], Hue[0.3475733393775312], Hue[0.371310018369813], Hue[0.371310018369813], Hue[0.39504669736209447`], Hue[0.39504669736209447`], Hue[0.42079523656844053`], Hue[0.42079523656844053`], Hue[0.44654377577478666`], Hue[0.44654377577478666`], Hue[0.4722923149811328], Hue[0.4722923149811328], Hue[0.49804085418747884`], Hue[0.49804085418747884`], Hue[-0.47621060660617504`], Hue[-0.47621060660617504`], Hue[-0.45046206739982897`], Hue[-0.45046206739982897`], Hue[-0.3989649889871367], Hue[-0.3989649889871367], Hue[-0.3749347835454424], Hue[-0.3749347835454424], Hue[-0.35090457810374825`], Hue[-0.35090457810374825`], Hue[-0.3028441672203599], Hue[-0.3028441672203599], Hue[-0.2067233454535833], Hue[-0.2067233454535833], Hue[-0.1806812797978248], Hue[-0.1806812797978248], Hue[-0.1546392141420662], Hue[-0.1546392141420662], Hue[-0.10255508283054904`], Hue[-0.10255508283054904`], Hue[-0.0765130171747904], Hue[-0.0765130171747904], Hue[-0.05047095151903178], Hue[-0.05047095151903178], Hue[0.0016131797924853512`], Hue[0.0016131797924853512`], Hue[0.027180309676497462`], Hue[0.027180309676497462`], Hue[0.052747439560509576`], Hue[0.052747439560509576`], Hue[0.0783145694445217], Hue[0.0783145694445217], Hue[0.1038816993285338], Hue[0.1038816993285338], Hue[0.1294488292125459], Hue[0.1294488292125459], Hue[0.15501595909655805`], Hue[0.15501595909655805`], Hue[0.18058308898057016`], Hue[0.18058308898057016`], Hue[0.20615021886458226`], Hue[0.20615021886458226`], Hue[0.22999901498394243`], Hue[0.22999901498394243`], Hue[0.25384781110330273`], Hue[0.25384781110330273`], Hue[0.2776966072226629], Hue[0.2776966072226629], Hue[0.30154540334202307`], Hue[0.30154540334202307`], Hue[0.32539419946138326`], Hue[0.32539419946138326`], Hue[0.3492429955807434], Hue[0.3492429955807434], Hue[0.37309179170010354`], Hue[0.37309179170010354`], Hue[0.39694058781946384`], Hue[0.39694058781946384`], Hue[0.42280124415288844`], Hue[0.42280124415288844`], Hue[0.448661900486313], Hue[0.448661900486313], Hue[0.47452255681973765`], Hue[0.47452255681973765`], Hue[-0.49961678684683786`], Hue[-0.49961678684683786`], Hue[-0.4737561305134133], Hue[-0.4737561305134133], Hue[-0.44789547417998865`], Hue[-0.44789547417998865`], Hue[-0.42203481784656405`], Hue[-0.42203481784656405`], Hue[-0.3961741615131395], Hue[-0.3961741615131395], Hue[-0.3720318389443668], Hue[-0.3720318389443668], Hue[-0.3478895163755941], Hue[-0.3478895163755941], Hue[-0.29960487123804874`], Hue[-0.29960487123804874`], Hue[-0.20303558096295804`], Hue[-0.20303558096295804`], Hue[-0.17936819416593183`], Hue[-0.17936819416593183`], Hue[-0.1557008073689056], Hue[-0.1557008073689056], Hue[-0.1083660337748532], Hue[-0.1083660337748532], Hue[-0.08469864697782699], Hue[-0.08469864697782699], Hue[-0.06103126018080077], Hue[-0.06103126018080077], Hue[-0.013696486586748354`], Hue[-0.013696486586748354`], Hue[0.011982760424342244`], Hue[0.011982760424342244`], Hue[0.03766200743543284], Hue[0.03766200743543284], Hue[0.08902050145761405], Hue[0.08902050145761405], Hue[0.11469974846870462`], Hue[0.11469974846870462`], Hue[0.14037899547979524`], Hue[0.14037899547979524`], Hue[0.19173748950197642`], Hue[0.19173748950197642`], Hue[0.2156984027484151], Hue[0.2156984027484151], Hue[0.2396593159948538], Hue[0.2396593159948538], Hue[0.26362022924129247`], Hue[0.26362022924129247`], Hue[0.2875811424877312], Hue[0.2875811424877312], Hue[0.3115420557341699], Hue[0.3115420557341699], Hue[0.3355029689806086], Hue[0.3355029689806086], Hue[0.3594638822270473], Hue[0.3594638822270473], Hue[0.38342479547348596`], Hue[0.38342479547348596`], Hue[0.40939756893398904`], Hue[0.40939756893398904`], Hue[0.4353703423944921], Hue[0.4353703423944921], Hue[0.46134311585499516`], Hue[0.46134311585499516`], Hue[0.4873158893154983], Hue[0.4873158893154983], Hue[-0.48671133722399873`], Hue[-0.48671133722399873`], Hue[-0.46073856376349565`], Hue[-0.46073856376349565`], Hue[-0.4347657903029926], Hue[-0.4347657903029926], Hue[-0.4087930168424895], Hue[-0.4087930168424895], Hue[-0.3832951791537329], Hue[-0.3832951791537329], Hue[-0.35779734146497616`], Hue[-0.35779734146497616`], Hue[-0.33229950377621964`], Hue[-0.33229950377621964`], Hue[-0.306801666087463], Hue[-0.306801666087463], Hue[-0.2813038283987063], Hue[-0.2813038283987063], Hue[-0.25580599070994964`], Hue[-0.25580599070994964`], Hue[-0.23030815302119298`], Hue[-0.23030815302119298`], Hue[-0.20481031533243646`], Hue[-0.20481031533243646`], Hue[-0.18103081140833188`], Hue[-0.18103081140833188`], Hue[-0.1572513074842272], Hue[-0.1572513074842272], Hue[-0.13347180356012248`], Hue[-0.13347180356012248`], Hue[-0.10969229963601777`], Hue[-0.10969229963601777`], Hue[-0.08591279571191303], Hue[-0.08591279571191303], Hue[-0.062133291787808326`], Hue[-0.062133291787808326`], Hue[-0.0383537878637036], Hue[-0.0383537878637036], Hue[-0.014574283939598892`], Hue[-0.014574283939598892`], Hue[0.011217080198570163`], Hue[0.011217080198570163`], Hue[0.03700844433673922], Hue[0.03700844433673922], Hue[0.06279980847490828], Hue[0.06279980847490828], Hue[0.08859117261307749], Hue[0.08859117261307749], Hue[0.11438253675124668`], Hue[0.11438253675124668`], Hue[0.14017390088941575`], Hue[0.14017390088941575`], Hue[0.1659652650275848], Hue[0.1659652650275848], Hue[0.19175662916575387`], Hue[0.19175662916575387`], Hue[0.21582965953927097`], Hue[0.21582965953927097`], Hue[0.2399026899127882], Hue[0.2399026899127882], Hue[0.26397572028630545`], Hue[0.26397572028630545`], Hue[0.28804875065982255`], Hue[0.28804875065982255`], Hue[0.31212178103333965`], Hue[0.31212178103333965`], Hue[0.3361948114068568], Hue[0.3361948114068568], Hue[0.36026784178037413`], Hue[0.36026784178037413`], Hue[0.3843408721538913], Hue[0.3843408721538913], Hue[0.41042576274147297`], Hue[0.41042576274147297`], Hue[0.4365106533290544], Hue[0.4365106533290544], Hue[0.46259554391663593`], Hue[0.46259554391663593`], Hue[0.4886804345042176], Hue[0.4886804345042176], Hue[-0.4852346749082007], Hue[-0.4852346749082007], Hue[-0.45914978432061926`], Hue[-0.45914978432061926`], Hue[-0.4330648937330378], Hue[-0.4330648937330378], Hue[-0.40698000314545607`], Hue[-0.40698000314545607`], Hue[-0.3813700483296211], Hue[-0.3813700483296211], Hue[-0.3557600935137859], Hue[-0.3557600935137859], Hue[-0.33015013869795073`], Hue[-0.33015013869795073`], Hue[-0.30454018388211557`], Hue[-0.30454018388211557`], Hue[-0.2789302290662803], Hue[-0.2789302290662803], Hue[-0.25332027425044534`], Hue[-0.25332027425044534`], Hue[-0.22771031943461043`], Hue[-0.22771031943461043`], Hue[-0.20210036461877523`], Hue[-0.20210036461877523`], Hue[-0.17820874356759198`], Hue[-0.17820874356759198`], Hue[-0.15431712251640872`], Hue[-0.15431712251640872`], Hue[-0.13042550146522575`], Hue[-0.13042550146522575`], Hue[-0.10653388041404252`], Hue[-0.10653388041404252`], Hue[-0.08264225936285922], Hue[-0.08264225936285922], Hue[-0.05875063831167625], Hue[-0.05875063831167625], Hue[-0.034859017260492994`], Hue[-0.034859017260492994`], Hue[-0.010967396209309739`], Hue[-0.010967396209309739`], Hue[0.014936085055937862`], Hue[0.014936085055937862`], Hue[0.04083956632118546], Hue[0.04083956632118546], Hue[0.06674304758643305], Hue[0.06674304758643305], Hue[0.09264652885168066], Hue[0.09264652885168066], Hue[0.11855001011692824`], Hue[0.11855001011692824`], Hue[0.1444534913821759], Hue[0.1444534913821759], Hue[0.17035697264742347`], Hue[0.17035697264742347`], Hue[0.19626045391267108`], Hue[0.19626045391267108`], Hue[0.22014339060293103`], Hue[0.22014339060293103`], Hue[0.24402632729319096`], Hue[0.24402632729319096`], Hue[0.26790926398345116`], Hue[0.26790926398345116`], Hue[0.2917922006737111], Hue[0.2917922006737111], Hue[0.31567513736397107`], Hue[0.31567513736397107`], Hue[0.3395580740542313], Hue[0.3395580740542313], Hue[0.3634410107444912], Hue[0.3634410107444912], Hue[0.3873239474347511]}], { AspectRatio -> GoldenRatio^(-1), Axes -> True, AxesLabel -> { Style["x", 24, Italic], Style[ Row[{"\[Psi](", Style["x", Italic], ")"}], 24]}, AxesOrigin -> {-3.75, 0}, Method -> {"AxesInFront" -> True}, PlotRange -> {{-3.75, 3.75}, {0, 2.1}}, PlotRangeClipping -> True, PlotRangePadding -> { Scaled[0.02], Automatic}, Ticks -> {{-3, 0, 3}, {0, 1, 2}}, TicksStyle -> Directive[20, GrayLevel[0.5]]}], $CellContext`m1 = Graphics[ GraphicsComplex[CompressedData[" 1:eJxFlHk01O8exzWyyzKGbDFmbNm7lSW+3+eJ8ouKnyVFXWloCJGlbKn4ETmW Kdn3H9mOLSoyab7ZQ1lqcCUke8oSEjG3e+694znnOc95/fm8P6/PW4HibX0Z x8HBEfv7/ucd91MZZLHUMI7/HcgqEDWoVWVz2F8EGWNEmc0DB0tULL6S2Txc 8qtnrViBzVEHIh6OUOXYHO5qH8fslmLz0QS8smc/gc0NEQ8WA2aEsbc6wIta uRuxyHiYR+7ixr4n++h7UtuRXrUGxX39PxkuchkXZnhC0K7t2VAN2keGUI5A 6hZrF5jYzGeZUCZB6TWCGbziCiKexOf0WG6DVza1kREdT8BhLtHEg5a8MC/a y1HFeARYUs06c/aJQt5I8es+5Gnw6GVsoucvcdivcORZxrFu0PMy8szBKGkY Et/peqY1Bei9SQ9w8JeHucL8LluehqD+VfXrBm4SzEP1lObnm9FVcmHUrQhF uKUlmIvPJqFh2FDx32vKsOyxFm9XrBOyrjPX2oTuh///b2wxj7h4nTqb/5u/ JpvvG0z5Z37Yz86nZ0ZT2PYyns3cNLHXpx0EsI8X6Hcnvd2R86k/pdI+7MLi swjqoVtKqDFThkTIWmTEVXAiNVcb0fUlOq7WrR60cJnIDknqA0P7KsugOytA P0WGoTzwALzQ9lyKo3NCc2Rz4X7CGzA30/vQ4PgeWDr0JeX54ykQjPfQ5o4T g1KHV0pW/jEG6tF7K91HJWHCnUyiX+kzsNuUNtW6JQsT5p6xaj57AXUCFn59 jAiXUvfatG5zgkHfMtXs42R4ZbDJTmIzADX0ham0BiV467alwlXNFuRF4Lhe jbQqTLrpanegfd2ocX79qmeIGjsPvfiUG/zDGmyu77+r/Pbqjq+8RrnSY1li bKbwvxum5O3BeiTq5tTP6yPvpdr+OWKzG5OZCFOnnVpH+O945qcarDKKAYuk 65+LWuAMG7ZXWxkjZSaltsVyQPNsuGXGgQVwT0SM2Ea6DVjNaUS6zy7YI5xB +ZdJIxAJWErU7eCHX8u5rxF9PwMXI4ct6zN4OOtMJuuemABV2/zH5OT3QqNK WylWWhNwxwnIhTbKwIU5imixZARwbjC9aHWaCM2DhF+EGCsAs3Ttn5qFJGjV fMLEKi8XlTz5PYFHQQnOUvnKXLtXkOxMx8XSaBUYatNAzGJqIh/jfaQlP+74 RMnobhE238knJYnO2a4hiv3Z9Etxj2WnUam47VN9MT6sp2aN54dfOtKsea6s qHWbseqtoloibo2u2iYfld81w1g4KzostDWOkoM3Rx0qB0F3mPMFixArMHY3 54ei20/wKmRh3ZdRAALT0UYnLm5YVdiJ/8DbD5odqpOMMGEYtljYdFFwBtBm Qi49byZAUy6m19vEAdByi+dRmIsUDIqzDefXKAbZ98QrRQzkYCTTfigx6QxY djcoTPNTgMl8U/5q1pMo9eT+c0KTZJg+wtJzuGiJOqbF5Uo5KMMQB07vyexE ZMiWeptepgq5LN3f3llvNBIMu6jC5bWzPxZKZ1lTz3b8KLhsT1Q+stM3tLZq 6tdmIYzGKZJTxEtE7g+VszhoXJiYd2R5q+cnxItJmBiK+sGoI2+EHibHoxsM k29Jke8ZNmvhS+ptIiB6f2LRgtkcmBcefHHUyg/kJujU9Z7igKsns05+G6CD 3w0g9jSWD+L+IGGmFz4Bh14rl6DnopCwL+VY0dzvnhrp9GiJk4ClsobSmrjX IMup3WBQUQaG3+G8aXwiAbBEY04zOInwBEFucFxCG+C0fD5dtyPBmvnzDwTH q9G7tV0CTX2K8FbfttdhNUGUVpHZVQhUoI7v/qBRX1NkbrR88Wvcjh8/8jyu 4nft+HGI4c8n9FqUncdg30HQpMuPDV1E6biJcCR7AB94I4cDu6/hql0SY4S+ YE015mfNM07WyI9xT/eheTdKc6PNusH3+9dydOjHgNBiEdlyZQ3M2u11GzTP BNKXmfYBY7thjOz3wGzDPjCgYCxODxeCn9b5XEiPpkFkqF/7qCoBPp8Yvia5 9gFgju1dqu8kYVTDKQ3VuirQO93X4ZGxD1LPVL/fE0wB8YybD3nUFGDHEVt6 7/AKKj/qDu2SyPCjuELqtzxntIvLVZYpoAx7xI5fX1ErRzqpBedrnVWhvnj/ pcCNEaO/ozbf8ijt+HHo9HfrwVBB7Io86Q2FaI1I2o/R6Xs5MYM/OTKbYkTQ QrVmit2XZUZfFddGeOpjtABfH2D6Vz7DaiZVWM1fHVxprAvJF1wGzpfFZGbC ooHjBu5eQTIOMo+UpM0GtYGtykuEOh5BWM8aWVYxmQTeRZRkjSU8tAx1Koqw GwdP5cxlA6r2wrwON8VC2ZdAr+A0juQkC9uujA5l6QaBNjdOn8/JRLhHezfN ogUPaNzfRKZWSTD16RoamByLlo5IEU55K8HoOv6yNb4RpDyGSKjsVYGuXY61 uZ5iyKYHbjuMJoIpaQXQtwVmjG6e81evWODBBLd9rv1QqkbMy2LcKBa/GIV4 lKDvREW1So9j6S6fGevBulpeFctoyHBP7frwGJjhvu4xPXkBVO9L6dz4sAn+ mAutjq8rB4NmogKjt0QgtrJcJjE2DdJtIjYeOInDNA8d42DPd6Aj2zR0aFUK mvfai2XK5wF39XOJT/vlYPw+5rxszglgJ7FWq96gAO9+eeT06CwTraid9m49 pAjnwyqo5Tf00UWNJ4qOxcow7EsDc6E9CJk1Vs1nrKqy5xcQ3HQbV7szz38D mWO1cA== "], {{{}, { EdgeForm[], RGBColor[0.88, 1, 0.88], GraphicsGroup[{ Polygon[{{96, 139, 76, 110, 41, 125, 59, 93, 22, 138, 75, 109, 40, 124, 58, 92, 21, 137, 74, 108, 39, 123, 57, 91, 20, 136, 73, 107, 38, 122, 56, 90, 19, 135, 72, 106, 37, 121, 55, 89, 18, 134, 71, 105, 36, 120, 54, 88, 17, 133, 70, 104, 35, 119, 53, 87, 16, 132, 69, 103, 34, 118, 52, 86, 15, 68, 102, 33, 117, 51, 85, 14, 131, 67, 101, 32, 116, 50, 84, 13, 130, 66, 100, 31, 115, 49, 83, 12, 129, 65, 99, 30, 114, 48, 82, 11, 128, 64, 98, 29, 113, 47, 81, 10, 127, 63, 97, 28, 112, 46, 80, 9, 126, 62}}]}]}, {}, {}}, {{}, {}, { Hue[0.67, 0.6, 0.6], RGBColor[0, 2/3, 0], Line[{1, 78, 44, 26, 2, 3, 4, 5, 6, 7, 8, 79, 45, 27, 96, 62, 126, 9, 80, 46, 112, 28, 97, 63, 127, 10, 81, 47, 113, 29, 98, 64, 128, 11, 82, 48, 114, 30, 99, 65, 129, 12, 83, 49, 115, 31, 100, 66, 130, 13, 84, 50, 116, 32, 101, 67, 131, 14, 85, 51, 117, 33, 102, 68, 15, 86, 52, 118, 34, 103, 69, 132, 16, 87, 53, 119, 35, 104, 70, 133, 17, 88, 54, 120, 36, 105, 71, 134, 18, 89, 55, 121, 37, 106, 72, 135, 19, 90, 56, 122, 38, 107, 73, 136, 20, 91, 57, 123, 39, 108, 74, 137, 21, 92, 58, 124, 40, 109, 75, 138, 22, 93, 59, 125, 41, 110, 76, 139, 23, 94, 60, 42, 24, 95, 61, 43, 111, 77, 140, 25}]}}}], { AspectRatio -> GoldenRatio^(-1), Axes -> True, AxesLabel -> { Style["p", 24, GrayLevel[0], Italic], Row[{ Style[ "\[LeftBracketingBar]\!\(\*OverscriptBox[\(\[Psi]\), \(~\)]\)", 24], Style["(p)", 24, Italic, GrayLevel[0]], Style[ "\!\(\*SuperscriptBox[\(\[LeftBracketingBar]\), \(2\)]\)", 24]}]}, AxesOrigin -> {-13.5, 0}, Method -> {"AxesInFront" -> True}, PlotRange -> {{-13.5, 15}, {0, 1.1}}, PlotRangeClipping -> True, PlotRangePadding -> { Scaled[0.02], Automatic}, Ticks -> {{-10, 0, 10}, {0, 0.5, 1, 1.5}}, TicksStyle -> Directive[20, GrayLevel[0.5]]}], $CellContext`psik[ Pattern[$CellContext`k, Blank[]], Pattern[$CellContext`k0, Blank[]], Pattern[$CellContext`x0, Blank[]], Pattern[$CellContext`a, Blank[]]] := (Sqrt[$CellContext`a]/Pi^(1/4)) E^(((-(1/ 2)) $CellContext`a^2) ($CellContext`k - $CellContext`k0)^2 - ( I $CellContext`k) $CellContext`x0), $CellContext`m2 = Graphics[{ Thickness[Large], RGBColor[0, 2/3, 0], Dashing[{Small, Small}], Line[{{4., 0}, {4., 1.}}]}], $CellContext`m3a = Style[ Row[{"\[LeftAngleBracket]", OverHat[ Style["p", Italic]], "\[RightAngleBracket] = ", NumberForm[4., {4, 2}]}], RGBColor[0, 2/3, 0], 18], $CellContext`m3b = Style[ Row[{"\[CapitalDelta]", Style["p", Italic], " = " NumberForm[0.7056953904057359, {4, 2}]}], 18], $CellContext`m3 = Graphics[ Text[ Column[{ Style[ Row[{"\[LeftAngleBracket]", OverHat[ Style["p", Italic]], "\[RightAngleBracket] = ", NumberForm[4., {4, 2}]}], RGBColor[0, 2/3, 0], 18], Style[ Row[{"\[CapitalDelta]", Style["p", Italic], " = " NumberForm[0.7056953904057359, {4, 2}]}], 18]}], {6.5, 0.85}]], $CellContext`k2plot = Graphics[{ GraphicsComplex[CompressedData[" 1:eJxFlHk01O8exzWyyzKGbDFmbNm7lSW+3+eJ8ouKnyVFXWloCJGlbKn4ETmW Kdn3H9mOLSoyab7ZQ1lqcCUke8oSEjG3e+694znnOc95/fm8P6/PW4HibX0Z x8HBEfv7/ucd91MZZLHUMI7/HcgqEDWoVWVz2F8EGWNEmc0DB0tULL6S2Txc 8qtnrViBzVEHIh6OUOXYHO5qH8fslmLz0QS8smc/gc0NEQ8WA2aEsbc6wIta uRuxyHiYR+7ixr4n++h7UtuRXrUGxX39PxkuchkXZnhC0K7t2VAN2keGUI5A 6hZrF5jYzGeZUCZB6TWCGbziCiKexOf0WG6DVza1kREdT8BhLtHEg5a8MC/a y1HFeARYUs06c/aJQt5I8es+5Gnw6GVsoucvcdivcORZxrFu0PMy8szBKGkY Et/peqY1Bei9SQ9w8JeHucL8LluehqD+VfXrBm4SzEP1lObnm9FVcmHUrQhF uKUlmIvPJqFh2FDx32vKsOyxFm9XrBOyrjPX2oTuh///b2wxj7h4nTqb/5u/ JpvvG0z5Z37Yz86nZ0ZT2PYyns3cNLHXpx0EsI8X6Hcnvd2R86k/pdI+7MLi swjqoVtKqDFThkTIWmTEVXAiNVcb0fUlOq7WrR60cJnIDknqA0P7KsugOytA P0WGoTzwALzQ9lyKo3NCc2Rz4X7CGzA30/vQ4PgeWDr0JeX54ykQjPfQ5o4T g1KHV0pW/jEG6tF7K91HJWHCnUyiX+kzsNuUNtW6JQsT5p6xaj57AXUCFn59 jAiXUvfatG5zgkHfMtXs42R4ZbDJTmIzADX0ham0BiV467alwlXNFuRF4Lhe jbQqTLrpanegfd2ocX79qmeIGjsPvfiUG/zDGmyu77+r/Pbqjq+8RrnSY1li bKbwvxum5O3BeiTq5tTP6yPvpdr+OWKzG5OZCFOnnVpH+O945qcarDKKAYuk 65+LWuAMG7ZXWxkjZSaltsVyQPNsuGXGgQVwT0SM2Ea6DVjNaUS6zy7YI5xB +ZdJIxAJWErU7eCHX8u5rxF9PwMXI4ct6zN4OOtMJuuemABV2/zH5OT3QqNK WylWWhNwxwnIhTbKwIU5imixZARwbjC9aHWaCM2DhF+EGCsAs3Ttn5qFJGjV fMLEKi8XlTz5PYFHQQnOUvnKXLtXkOxMx8XSaBUYatNAzGJqIh/jfaQlP+74 RMnobhE238knJYnO2a4hiv3Z9Etxj2WnUam47VN9MT6sp2aN54dfOtKsea6s qHWbseqtoloibo2u2iYfld81w1g4KzostDWOkoM3Rx0qB0F3mPMFixArMHY3 54ei20/wKmRh3ZdRAALT0UYnLm5YVdiJ/8DbD5odqpOMMGEYtljYdFFwBtBm Qi49byZAUy6m19vEAdByi+dRmIsUDIqzDefXKAbZ98QrRQzkYCTTfigx6QxY djcoTPNTgMl8U/5q1pMo9eT+c0KTZJg+wtJzuGiJOqbF5Uo5KMMQB07vyexE ZMiWeptepgq5LN3f3llvNBIMu6jC5bWzPxZKZ1lTz3b8KLhsT1Q+stM3tLZq 6tdmIYzGKZJTxEtE7g+VszhoXJiYd2R5q+cnxItJmBiK+sGoI2+EHibHoxsM k29Jke8ZNmvhS+ptIiB6f2LRgtkcmBcefHHUyg/kJujU9Z7igKsns05+G6CD 3w0g9jSWD+L+IGGmFz4Bh14rl6DnopCwL+VY0dzvnhrp9GiJk4ClsobSmrjX IMup3WBQUQaG3+G8aXwiAbBEY04zOInwBEFucFxCG+C0fD5dtyPBmvnzDwTH q9G7tV0CTX2K8FbfttdhNUGUVpHZVQhUoI7v/qBRX1NkbrR88Wvcjh8/8jyu 4nft+HGI4c8n9FqUncdg30HQpMuPDV1E6biJcCR7AB94I4cDu6/hql0SY4S+ YE015mfNM07WyI9xT/eheTdKc6PNusH3+9dydOjHgNBiEdlyZQ3M2u11GzTP BNKXmfYBY7thjOz3wGzDPjCgYCxODxeCn9b5XEiPpkFkqF/7qCoBPp8Yvia5 9gFgju1dqu8kYVTDKQ3VuirQO93X4ZGxD1LPVL/fE0wB8YybD3nUFGDHEVt6 7/AKKj/qDu2SyPCjuELqtzxntIvLVZYpoAx7xI5fX1ErRzqpBedrnVWhvnj/ pcCNEaO/ozbf8ijt+HHo9HfrwVBB7Io86Q2FaI1I2o/R6Xs5MYM/OTKbYkTQ QrVmit2XZUZfFddGeOpjtABfH2D6Vz7DaiZVWM1fHVxprAvJF1wGzpfFZGbC ooHjBu5eQTIOMo+UpM0GtYGtykuEOh5BWM8aWVYxmQTeRZRkjSU8tAx1Koqw GwdP5cxlA6r2wrwON8VC2ZdAr+A0juQkC9uujA5l6QaBNjdOn8/JRLhHezfN ogUPaNzfRKZWSTD16RoamByLlo5IEU55K8HoOv6yNb4RpDyGSKjsVYGuXY61 uZ5iyKYHbjuMJoIpaQXQtwVmjG6e81evWODBBLd9rv1QqkbMy2LcKBa/GIV4 lKDvREW1So9j6S6fGevBulpeFctoyHBP7frwGJjhvu4xPXkBVO9L6dz4sAn+ mAutjq8rB4NmogKjt0QgtrJcJjE2DdJtIjYeOInDNA8d42DPd6Aj2zR0aFUK mvfai2XK5wF39XOJT/vlYPw+5rxszglgJ7FWq96gAO9+eeT06CwTraid9m49 pAjnwyqo5Tf00UWNJ4qOxcow7EsDc6E9CJk1Vs1nrKqy5xcQ3HQbV7szz38D mWO1cA== "], {{{}, { EdgeForm[], RGBColor[0.88, 1, 0.88], GraphicsGroup[{ Polygon[{{96, 139, 76, 110, 41, 125, 59, 93, 22, 138, 75, 109, 40, 124, 58, 92, 21, 137, 74, 108, 39, 123, 57, 91, 20, 136, 73, 107, 38, 122, 56, 90, 19, 135, 72, 106, 37, 121, 55, 89, 18, 134, 71, 105, 36, 120, 54, 88, 17, 133, 70, 104, 35, 119, 53, 87, 16, 132, 69, 103, 34, 118, 52, 86, 15, 68, 102, 33, 117, 51, 85, 14, 131, 67, 101, 32, 116, 50, 84, 13, 130, 66, 100, 31, 115, 49, 83, 12, 129, 65, 99, 30, 114, 48, 82, 11, 128, 64, 98, 29, 113, 47, 81, 10, 127, 63, 97, 28, 112, 46, 80, 9, 126, 62}}]}]}, {}, {}}, {{}, {}, { Hue[0.67, 0.6, 0.6], RGBColor[0, 2/3, 0], Line[{1, 78, 44, 26, 2, 3, 4, 5, 6, 7, 8, 79, 45, 27, 96, 62, 126, 9, 80, 46, 112, 28, 97, 63, 127, 10, 81, 47, 113, 29, 98, 64, 128, 11, 82, 48, 114, 30, 99, 65, 129, 12, 83, 49, 115, 31, 100, 66, 130, 13, 84, 50, 116, 32, 101, 67, 131, 14, 85, 51, 117, 33, 102, 68, 15, 86, 52, 118, 34, 103, 69, 132, 16, 87, 53, 119, 35, 104, 70, 133, 17, 88, 54, 120, 36, 105, 71, 134, 18, 89, 55, 121, 37, 106, 72, 135, 19, 90, 56, 122, 38, 107, 73, 136, 20, 91, 57, 123, 39, 108, 74, 137, 21, 92, 58, 124, 40, 109, 75, 138, 22, 93, 59, 125, 41, 110, 76, 139, 23, 94, 60, 42, 24, 95, 61, 43, 111, 77, 140, 25}]}}}], { Thickness[Large], RGBColor[0, 2/3, 0], Dashing[{Small, Small}], Line[{{4., 0}, {4., 1.}}]}, Text[ Column[{ Style[ Row[{"\[LeftAngleBracket]", OverHat[ Style["p", Italic]], "\[RightAngleBracket] = ", NumberForm[4., {4, 2}]}], RGBColor[0, 2/3, 0], 18], Style[ Row[{"\[CapitalDelta]", Style["p", Italic], " = " NumberForm[0.7056953904057359, {4, 2}]}], 18]}], {6.5, 0.85}]}, { AspectRatio -> GoldenRatio^(-1), Axes -> True, AxesLabel -> { Style["p", 24, GrayLevel[0], Italic], Row[{ Style[ "\[LeftBracketingBar]\!\(\*OverscriptBox[\(\[Psi]\), \(~\)]\)", 24], Style["(p)", 24, Italic, GrayLevel[0]], Style[ "\!\(\*SuperscriptBox[\(\[LeftBracketingBar]\), \(2\)]\)", 24]}]}, AxesOrigin -> {-13.5, 0}, Method -> {"AxesInFront" -> True}, PlotRange -> {{-13.5, 15}, {0, 1.1}}, PlotRangeClipping -> True, PlotRangePadding -> { Scaled[0.02], Automatic}, Ticks -> {{-10, 0, 10}, {0, 0.5, 1, 1.5}}, TicksStyle -> Directive[20, GrayLevel[0.5]]}], $CellContext`kplot = Graphics[ GraphicsComplex[CompressedData[" 1:eJx12Gs4lekaB3ARcshxKSIWyymHanZTUdb7PFGmVIySoraMREWklCQVQ6cr rFLOx0nIRQdNUSuz1iAUk8MM2RI6OCRFhUSsPXPtfS+fbl9cv4/rfZ/3uf// W98rcNNuSQkJCf8ZEhL//H91yKRVJDITSvz/j4pyVK1LTMWO+Jmlbcs1FvvZ kusmju85Yrdf/9Ywmq8v9pnvoi53+OiKHenrFtNcryX2qjg1Y/8WlthlUZeG QvqUhU8XkwCfmzO5jqmXszl1MsLPCUFW/j413EazMsP5LV8F3rqpO/pkw5i6 qbfhFrwXAqVMhaRJ0QzyZuKqyM6rmxQcYK2je31J1K+xmQ1OU+T3zSXRUU9+ JUulVeOXOM2i2WcDPExsO4iTz7razPmqdFa0xuEgTi+59tuFeP9vGrRFf8W9 1NX1pOG36C1LzsyjYbG1vluqEsnyP1JC3IP1aJayvPek/0ry4Pfix2UyBjSb WW40MFDJjHByz5yIMqSTCxWz1DIMmAhhW/4vo8a08PbCWXUXPLlji/urKpgF FH7vhXxZDY1Sc7H/9/wtxb5o3ROc9nyB+Pk09Fkqu+xWE1uGp/54o7uC8MUO /unuwH3c7UlftZKfzxDGprPMwyeNGNtmbQNW+pAg5oYU987+cmbsI1+yZM8D 8kjaTqdN04qsdLvlFHpqmFglaguMn10iDxf5f4zhS1EH7sTgxbg/SH9f42Xr NbNpQdu7xPu3e8gxNb9FMjHqVGvp8PXhf3WRB8y54fpVmjTuVBr7UME9MtOe 11M1qUPj+u+J7rwOIOYsYeThLjb9mDR3c9WUFGk9WGiasYZD97ZWuM6ZCGFW HqRJvDIjeuKkk/5+y0fch0dfLb8zz5ReOe7r+l3NmE35wNh+/zAz8fNYHpt4 RL7dQuwHLaeNn+6fPq+zbLLmdaWri+0l/2e7V/ZsYcOc0n7z7Vbcv7Sq/92x eaZQ+02EOW/DGFf+lP/VJOsRQT4RGSwLzmIcJVeWTY1UCToK7Qpc8nWJ5dZI p9TvBsk5FXV2tcFJIqpMZvODZtAG5VSv/9iVE5WQj/HLnsjT90UyB9gHXxNv G/fJTVvU6NtdHM6ytW/IrSn51bp6c6nNTRctUXIF2SepoBterk0H+71U8zWj yK4y+53OG9nUIVT5YZitPlmXsuirZa4Bda5ca+ecncVorv8cJ6tvRN/6yBX6 1g9zM9I8hgrOmtDwzWXs9GZL7ovYoHmaL6bPk1dq/SNlh+nnk3iFL1VjoSr8 seKb4WynWpsCDZe7VupywoY7o7JfDqVwKy23FeZVTQlGAk1Mr2tsYkZcElbp zegTDG5VbVeafMVwjk10ut9sJfURu3Y4hjmTrtOZXwz3fCW/hw2OHRTkkKMp TLmntAy9lVur9nxWC6l0L75iI1SmEUO5FTsV+wivL+yn+5Usai/dHPA0/hl5 dEL2WoS3Fg2NcYmUt8gnGec0bqpY69LoZre2+CtbyKd91rnJh/RpglxPsNmm bsZn/YJtSt0cmtIhWu6+04nxSI7J0nI3pmHuUoHdGfHcNhefk/xCUyrttO/p qbFyG8WInSbSAdPfj6PRVlHPvenzkbPbjW28Yvq+4VUX+7yvVBLypFQy82ax uRfbikQSPGmhemB0UZX/S25AM+tN25kvglLOePhSTiwzLrD7cCX6L8Hm0ciP 5tUq5OyC+LzBdf1kQLn14SrnQyQrbnFp4wYJOrI+ff2HZ3zy9w2gfveCHJX8 wUBov+MlcW909g69r0pZ8xNX5/X/fU911Po9iplDC3RWzrOUfEzSPWusWw21 aeQpqeO2a+OISPX8RoEUm65l6ba+mrOISC4MennY1YDeGdh+SfFVMXO6pE6h osmQnmiaClhqpsjwbqTV5RITuvjggtDOg/bc/s6iofcx0+fjS7bffrUZ0+fj e0GwnNJjVfHzaG1aQiqWyQvbdjJ8yTeR3IxnakePZEoIL1r4Lrp+3oZ5KOop v5o+IFh/R69LpreJyT5SkHV2XT35fPFA5mL+aqI0lMdxGh4lb13n7ml1SCPz dje7hXTNpOd1Ph/NWNlEnunbavAjlejLMTlvg2u9JDr8UE2nKYvef9N+QHP0 ORF61NSZ/qlJz5RtsDAtvUUae5ue+KXOpz5biv+afcyLxAqOX5Y106dPVrjw G9uHGb3OfdT1Coe+0NBP+pC9i6mT9tVpVjCmDeprDg+bFXFrfXK2l+wypVYa LT8dHe+w+eXMxFNZo+nz8f3Gz5tawxWFe/UM/vBib+JqunXx+XOlhNY/SqRV nFdhcs0qvVzffRI03ZIej0y6zeSoPQix//mqwLkvSdks2JzsLS8Nu6r4ieza ra7dF3GWeIxLnstJkKTNK64nvw2tJpM3f2KVyirSB6KOTyZ23SQwzyvB4qMa dQr3zItyfUXu6jrohNyaS7Of7DHM1fmNLM/ZKGngqUOr93a2pS8LJdV7pIJe J7Dp7EUzeY6P1AhP5oNKz4gBTbo7yhxNuMAUdGixNgQa0bOl8oWjch3covNs 1s1GE+pb51GS5a/OnfCTnIrgqQiNFobwpxT6bI5vCza/MSgrVJwKOvDFqJjr UHh+j5fjN0GuGsOy8vRhFhasEaZ4vxaMHVu2MODGJyasvaFkrL2L9Mkc9uvt 3kGK5yfWjj+fID/0hxfHlhaR1nWqCp0nVKhw+FPhnK5ekrI5avySpwZN9lts e8z/T/Ikwz68bUSLOjS6qafpZZN95tvi77bo0tj5zQM6mWuJ65zREvMyfXr6 3TXPa1ubmRslvYFV3xvSgYgbPkVHrJghi18NPfKNacS7subBmlDuW1vTq4IR U/H7CzlWcVKyZPp9wn2HGZ4HZsgfmOG+wAzzBjOcN8wwzzHD94kZ7nfM8P4x Q97CDPcjZpivmOH7wgz5BTPcR5hhnmGG844Z8iVmmAeYIU9ghvsEM+Q1zHD/ Yob5jRm+b8yQpzHD/MMM+Qkz3J+YIZ9ihnmDGfIKZrjPMEN/wAzzHjPkRcww LzBDHscM8xUz5DPMcH9jhr6EGfINZsjHmGE+Yob+gRnyBGbIo5ih/2GGvIYZ 8j5mmPeYoU9hhnyEGfI1ZpjHmKHvYoZ8ihn6DWbIN5ihP2KGPIgZ+gRmyB+Y od9jhjyOGfocZshzmKEvY4b8ixn6E2bIW5hhn4EZ+gdm6K+YIb9ihv0AZsj7 mKEvYoZ8iRn2N5ihb2GGvo4Z8jpm2Idghn6DGfoxZsjTmGFfhRn6JWbYT2CG foIZ9j+Yoc9hhn0AZugPmGE/hxn6NGbYx2CGPoYZ9l2Yob9ihv0HZuhLmGEf iRn2B5hh/4QZ+idm2O9hhr6OGfY9mP8Lj2X85A== "], {{{ EdgeForm[], GrayLevel[0.5], GraphicsGroup[{ Polygon[{{96, 141, 62}, {76, 364, 139}}], Polygon[CompressedData[" 1:eJwt1GOQXUEQhuGZ2LY3tq2NzY2dbGzbxo/Ytm3btm3bfru6fzxVX/WZHp1z b0Bwx6AOIZxzHREKI5DEO5cUMchVMBlTkBmFMRbjMMCMxwSER1UsxhJksdpE TLK5ZI6pmIZOGIj5WIAIVpuOGUiEJpiNOQg0czHPemXMTMyysYOxHwcQyeZc iEW2t6LYi302dhDWYwMiIjFWYhWCzWqsQRF0xnKssLFyxqVYZs9kjo3YhCA0 xW7ssbWlthlbkBVdsB075N7NTuyyXhmzFdtsrOxhLdbZ3uWMB3EI1dAdz/EC AWiG0ziDYsiGoziGruY4TiCpjTmLcxhitZM4ZXNJ7TwuIDKS4SZuoTmq4zKu IDu64Tpu2NiW+IlfKGlzXMQl65UzHMYR26vMeRt3UBxDcR8PEMXO+BKv0AI1 8BhPkMM8xTO7G+l5iEc2Vua8i3s2t8zxGm9QAj3wFd+Q3Gpv8Q5RURMf8Qk5 zWd8sV4Z8x4fbKz8ppLx2wpAHZvzO37Y3XRAG561RQVyL8Qhx0VKck+EIYdF CnI0OLJHLae1cOTwaOW0FoIcErnIpRCJHBnDydFlDnJ01CbXlfdGzoG8TueI QI7otVd6opCjeu2VnhjkmMjttCenrIU+TtcMRQ7tde9yhnjk+GjtVAJyQpR2 didyNuRxWktETuz1v0lqKcmp0NvpmrHIsb3eVSqkJadDG3IZZCRnwkhyTGQl Z/N6VpkjNTmN117pSU/O4LVXejKTs3jtlW/6Kq45/bbljLllr0gta8udyLtF e9kbipCLoh55FAqTA70+k5685Hzyzp2OKUYuLjWntfzkAijrtFaCXBJ9ycPw F//sW0gjZ5axaOd0TCm5W6/PpFaOXB7lnKpArojRTvdcV/YqY5yuWZBcyOve Y6MKuSrqy95QnVwD/Zz21Cc3wBintZrybXq9G6k1JDdCHKdrViJX9jp3AwST m8qZyf3RgtxS3qnTNYPI1byuLXM0Jjfx2is9zcjNvfZKTyv51rz+tuQ/5zf+ 2N39B7nCs3M= "]]}]}}, {{}, {}, { Hue[0.67, 0.6, 0.6], RGBColor[0, 2/3, 0], Line[{1, 78, 44, 26, 2, 3, 4, 5, 6, 7, 8, 79, 45, 27, 96, 62, 126, 9, 80, 46, 112, 28, 97, 63, 127, 10, 81, 47, 113, 29, 98, 64, 128, 11, 82, 48, 114, 30, 99, 65, 129, 12, 83, 49, 115, 31, 100, 66, 130, 13, 84, 50, 116, 32, 101, 67, 131, 14, 85, 51, 117, 33, 102, 68, 15, 86, 52, 118, 34, 103, 69, 132, 16, 87, 53, 119, 35, 104, 70, 133, 17, 88, 54, 120, 36, 105, 71, 134, 18, 89, 55, 121, 37, 106, 72, 135, 19, 90, 56, 122, 38, 107, 73, 136, 20, 91, 57, 123, 39, 108, 74, 137, 21, 92, 58, 124, 40, 109, 75, 138, 22, 93, 59, 125, 41, 110, 76, 139, 23, 94, 60, 42, 24, 95, 61, 43, 111, 77, 140, 25}, VertexColors -> Automatic]}}}, VertexColors -> { Hue[-0.14859154274409203`], Hue[0.03318592844698736], Hue[0.23025353726495593`], Hue[0.4142618094715702], Hue[-0.40533943018708873`], Hue[-0.20965053221885838`], Hue[-0.027020970861982595`], Hue[0.17089872812178267`], Hue[0.3652089152402747], Hue[-0.4535402342525878], Hue[-0.25699924611856095`], Hue[-0.07351759459588854], Hue[0.10635454506151062`], Hue[0.3015168223457992], Hue[0.4836197630187333], Hue[-0.3189871586814434], Hue[-0.1252035922468932], Hue[0.05552063757630247], Hue[0.25153500502638765`], Hue[0.4344900358651184], Hue[-0.36726479566926173`], Hue[-0.17262913906891506`], Hue[0.008947180920077307], Hue[0.20581363853595885`], Hue[0.38732395738193504`], Hue[-0.05770280714855234], Hue[0.26805382168102865`], Hue[0.45583434049384347`], Hue[-0.3552697401855744], Hue[-0.16525842035722474`], Hue[0.016418475232811054`], Hue[0.20393568370365492`], Hue[0.3925682926822663], Hue[-0.417683697831355], Hue[-0.2220953754641683], Hue[-0.03484147733529545], Hue[0.1535278213013451], Hue[0.34301252044575314`], Hue[-0.4663873799020715], Hue[-0.2699469673690884], Hue[-0.08184097907441902], Hue[0.10738040972801809`], Hue[0.296568797958947], Hue[-0.10314717494632232`], Hue[0.21947627490140573`], Hue[0.41052162786705904`], Hue[-0.4044049872190811], Hue[-0.21112883323789286`], Hue[-0.028549559681538744`], Hue[0.15514511438258277`], Hue[0.34704255751403273`], Hue[-0.4670319674063109], Hue[-0.2705412670728059], Hue[-0.08002253479109425], Hue[0.10452422943882379`], Hue[0.2972737627360703], Hue[0.48405132798152345`], Hue[-0.31860588151917507`], Hue[-0.12723505907166716`], Hue[0.05816379532404768], Hue[0.25119121824745305`], Hue[0.3166313684606517], Hue[-0.49885294687937226`], Hue[-0.30613449315206764`], Hue[-0.11938800747655665`], Hue[0.06138651014716085], Hue[0.25272625302472707`], Hue[0.4380940278504997], Hue[-0.3683354282563992], Hue[-0.1736494838555307], Hue[0.010339580120503516`], Hue[0.20253141316386644`], Hue[0.3887512781554356], Hue[-0.41682608778566677`], Hue[-0.22128805321900172`], Hue[-0.03644689907717086], Hue[0.3419463776704409], Hue[-0.12586935884520717`], Hue[0.19518750151159425`], Hue[0.38786527155366685`], Hue[-0.4289726107358345], Hue[-0.23406403967822692`], Hue[-0.051033577138713655`], Hue[0.1307498297220467], Hue[0.32427968992991596`], Hue[-0.4917061021937889], Hue[-0.29476421287712457`], Hue[-0.10261306351899382`], Hue[0.08002243350756312], Hue[0.2744043838812289], Hue[0.4592706819233211], Hue[-0.34293533859421854`], Hue[-0.14993209907029098`], Hue[0.03355548812206236], Hue[0.22850242839170595`], Hue[0.2923425950708401], Hue[0.47849069680723566`], Hue[-0.330702116668821], Hue[-0.14232321391689068`], Hue[0.038902492689985954`], Hue[0.22833096836419103`], Hue[0.415331160266383], Hue[-0.3930095630438772], Hue[-0.1978724296598495], Hue[-0.012250948607395895`], Hue[0.1780296172326058], Hue[0.3658818993005943], Hue[-0.44160673384386917`], Hue[-0.2456175102940452], Hue[-0.05914393907579493], Hue[0.31925758781469404`], Hue[0.4331779841804512], Hue[-0.37983736370232773`], Hue[-0.1881936267975588], Hue[-0.006065542224363848], Hue[0.17954039904311886`], Hue[0.36980542509814956`], Hue[-0.442357832618833], Hue[-0.2463183212684871], Hue[-0.057432006063194846`], Hue[0.12902602537008445`], Hue[0.3201431415909117], Hue[-0.4911680259602742], Hue[-0.2942764244441316], Hue[-0.10453801907304307`], Hue[0.3409201418504632], Hue[-0.47619659056598], Hue[-0.2815668696353143], Hue[-0.0964528010362226], Hue[0.08387052760433575], Hue[0.27712153768526315`], Hue[-0.3436612934689214], Hue[-0.14942653805121203`], Hue[0.032930108848402924`], Hue[0.22703320909512698`], Hue[0.411620657010277], Hue[-0.39204544172746414`], Hue[-0.19695859614395825`], Hue[-0.013749859078546771`], Hue[0.36463516752618796`], Hue[0.3166313684606517], Hue[0.3166313684606517], Hue[0.3409201418504632], Hue[0.3409201418504632], Hue[0.3652089152402747], Hue[0.3652089152402747], Hue[0.38786527155366685`], Hue[0.38786527155366685`], Hue[0.41052162786705904`], Hue[0.41052162786705904`], Hue[0.4331779841804512], Hue[0.4331779841804512], Hue[0.45583434049384347`], Hue[0.45583434049384347`], Hue[0.47849069680723566`], Hue[0.47849069680723566`], Hue[-0.49885294687937226`], Hue[-0.49885294687937226`], Hue[-0.47619659056598], Hue[-0.47619659056598], Hue[-0.4535402342525878], Hue[-0.4535402342525878], Hue[-0.4289726107358345], Hue[-0.4289726107358345], Hue[-0.4044049872190811], Hue[-0.4044049872190811], Hue[-0.37983736370232773`], Hue[-0.37983736370232773`], Hue[-0.3552697401855744], Hue[-0.3552697401855744], Hue[-0.330702116668821], Hue[-0.330702116668821], Hue[-0.30613449315206764`], Hue[-0.30613449315206764`], Hue[-0.2815668696353143], Hue[-0.2815668696353143], Hue[-0.25699924611856095`], Hue[-0.25699924611856095`], Hue[-0.23406403967822692`], Hue[-0.23406403967822692`], Hue[-0.21112883323789286`], Hue[-0.21112883323789286`], Hue[-0.1881936267975588], Hue[-0.1881936267975588], Hue[-0.16525842035722474`], Hue[-0.16525842035722474`], Hue[-0.14232321391689068`], Hue[-0.14232321391689068`], Hue[-0.11938800747655665`], Hue[-0.11938800747655665`], Hue[-0.0964528010362226], Hue[-0.0964528010362226], Hue[-0.07351759459588854], Hue[-0.07351759459588854], Hue[-0.051033577138713655`], Hue[-0.051033577138713655`], Hue[-0.028549559681538744`], Hue[-0.028549559681538744`], Hue[-0.006065542224363848], Hue[-0.006065542224363848], Hue[0.016418475232811054`], Hue[0.016418475232811054`], Hue[0.038902492689985954`], Hue[0.038902492689985954`], Hue[0.06138651014716085], Hue[0.06138651014716085], Hue[0.08387052760433575], Hue[0.08387052760433575], Hue[0.10635454506151062`], Hue[0.10635454506151062`], Hue[0.1307498297220467], Hue[0.1307498297220467], Hue[0.15514511438258277`], Hue[0.15514511438258277`], Hue[0.17954039904311886`], Hue[0.17954039904311886`], Hue[0.20393568370365492`], Hue[0.20393568370365492`], Hue[0.22833096836419103`], Hue[0.22833096836419103`], Hue[0.25272625302472707`], Hue[0.25272625302472707`], Hue[0.27712153768526315`], Hue[0.27712153768526315`], Hue[0.3015168223457992], Hue[0.3015168223457992], Hue[0.32427968992991596`], Hue[0.32427968992991596`], Hue[0.34704255751403273`], Hue[0.34704255751403273`], Hue[0.36980542509814956`], Hue[0.36980542509814956`], Hue[0.3925682926822663], Hue[0.3925682926822663], Hue[0.415331160266383], Hue[0.415331160266383], Hue[0.4380940278504997], Hue[0.4380940278504997], Hue[0.4836197630187333], Hue[0.4836197630187333], Hue[-0.4917061021937889], Hue[-0.4917061021937889], Hue[-0.4670319674063109], Hue[-0.4670319674063109], Hue[-0.442357832618833], Hue[-0.442357832618833], Hue[-0.417683697831355], Hue[-0.417683697831355], Hue[-0.3930095630438772], Hue[-0.3930095630438772], Hue[-0.3683354282563992], Hue[-0.3683354282563992], Hue[-0.3436612934689214], Hue[-0.3436612934689214], Hue[-0.3189871586814434], Hue[-0.3189871586814434], Hue[-0.29476421287712457`], Hue[-0.29476421287712457`], Hue[-0.2705412670728059], Hue[-0.2705412670728059], Hue[-0.2463183212684871], Hue[-0.2463183212684871], Hue[-0.2220953754641683], Hue[-0.2220953754641683], Hue[-0.1978724296598495], Hue[-0.1978724296598495], Hue[-0.1736494838555307], Hue[-0.1736494838555307], Hue[-0.14942653805121203`], Hue[-0.14942653805121203`], Hue[-0.1252035922468932], Hue[-0.1252035922468932], Hue[-0.10261306351899382`], Hue[-0.10261306351899382`], Hue[-0.08002253479109425], Hue[-0.08002253479109425], Hue[-0.057432006063194846`], Hue[-0.057432006063194846`], Hue[-0.03484147733529545], Hue[-0.03484147733529545], Hue[-0.012250948607395895`], Hue[-0.012250948607395895`], Hue[0.010339580120503516`], Hue[0.010339580120503516`], Hue[0.032930108848402924`], Hue[0.032930108848402924`], Hue[0.05552063757630247], Hue[0.05552063757630247], Hue[0.08002243350756312], Hue[0.08002243350756312], Hue[0.10452422943882379`], Hue[0.10452422943882379`], Hue[0.12902602537008445`], Hue[0.12902602537008445`], Hue[0.1535278213013451], Hue[0.1535278213013451], Hue[0.1780296172326058], Hue[0.1780296172326058], Hue[0.20253141316386644`], Hue[0.20253141316386644`], Hue[0.22703320909512698`], Hue[0.22703320909512698`], Hue[0.25153500502638765`], Hue[0.25153500502638765`], Hue[0.2744043838812289], Hue[0.2744043838812289], Hue[0.2972737627360703], Hue[0.2972737627360703], Hue[0.3201431415909117], Hue[0.3201431415909117], Hue[0.34301252044575314`], Hue[0.34301252044575314`], Hue[0.3658818993005943], Hue[0.3658818993005943], Hue[0.3887512781554356], Hue[0.3887512781554356], Hue[0.411620657010277], Hue[0.411620657010277], Hue[0.4344900358651184], Hue[0.4344900358651184], Hue[0.4592706819233211], Hue[0.4592706819233211], Hue[0.48405132798152345`], Hue[0.48405132798152345`], Hue[-0.4911680259602742], Hue[-0.4911680259602742], Hue[-0.4663873799020715], Hue[-0.4663873799020715], Hue[-0.44160673384386917`], Hue[-0.44160673384386917`], Hue[-0.41682608778566677`], Hue[-0.41682608778566677`], Hue[-0.39204544172746414`], Hue[-0.39204544172746414`], Hue[-0.36726479566926173`], Hue[-0.36726479566926173`], Hue[-0.34293533859421854`], Hue[-0.34293533859421854`], Hue[-0.31860588151917507`], Hue[-0.31860588151917507`], Hue[-0.2942764244441316], Hue[-0.2942764244441316], Hue[-0.2699469673690884], Hue[-0.2699469673690884], Hue[-0.2456175102940452], Hue[-0.2456175102940452], Hue[-0.22128805321900172`], Hue[-0.22128805321900172`], Hue[-0.19695859614395825`], Hue[-0.19695859614395825`], Hue[-0.17262913906891506`], Hue[-0.17262913906891506`], Hue[-0.14993209907029098`], Hue[-0.14993209907029098`], Hue[-0.12723505907166716`], Hue[-0.12723505907166716`], Hue[-0.10453801907304307`], Hue[-0.10453801907304307`], Hue[-0.08184097907441902], Hue[-0.08184097907441902], Hue[-0.05914393907579493], Hue[-0.05914393907579493], Hue[-0.03644689907717086], Hue[-0.03644689907717086]}], { AspectRatio -> GoldenRatio^(-1), Axes -> True, AxesLabel -> { Style["p", 24, Italic], Style[ Row[{"\!\(\*OverscriptBox[\(\[Psi]\), \(~\)]\)(", Style["p", Italic], ")"}], 24]}, AxesOrigin -> {-13.5, 0}, Method -> {"AxesInFront" -> True}, PlotRange -> {{-13.5, 15}, {0, 1.1}}, PlotRangeClipping -> True, PlotRangePadding -> { Scaled[0.02], Automatic}, Ticks -> {{-10, 0, 10}, {0, 0.5, 1, 1.5}}, TicksStyle -> Directive[20, GrayLevel[0.5]]}], Attributes[Subscript] = {NHoldRest}}; Typeset`initDone$$ = True); ReleaseHold[ HoldComplete[{$CellContext`psix[ Pattern[$CellContext`x, Blank[]], Pattern[$CellContext`k0, Blank[]], Pattern[$CellContext`x0, Blank[]], Pattern[$CellContext`a, Blank[]]] := (1/(Pi^(1/4) Sqrt[$CellContext`a])) Exp[I $CellContext`k0 $CellContext`x] Exp[(-($CellContext`x - $CellContext`x0)^2)/( 2 $CellContext`a^2)], $CellContext`psik[ Pattern[$CellContext`k, Blank[]], Pattern[$CellContext`k0, Blank[]], Pattern[$CellContext`x0, Blank[]], Pattern[$CellContext`a, Blank[]]] := (Sqrt[$CellContext`a]/Pi^(1/4)) E^((-(1/2)) $CellContext`a^2 ($CellContext`k - $CellContext`k0)^2 - I $CellContext`k $CellContext`x0)}]]; Typeset`initDone$$ = True), SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellID->512058499], Cell[TextData[{ "This Demonstration considers a Gaussian wavepacket ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"\[Psi]", "(", "x", ")"}], "=", RowBox[{ FractionBox["1", SqrtBox[ RowBox[{"a", " ", SuperscriptBox["\[Pi]", RowBox[{"1", "/", "2"}]]}]]], SuperscriptBox["e", RowBox[{"\[ImaginaryI]", " ", RowBox[{ RowBox[{ SubscriptBox["p", "0"], "(", RowBox[{"x", "-", SubscriptBox["x", "0"]}], ")"}], "/", "\[HBar]"}]}]], " ", SuperscriptBox["e", RowBox[{ RowBox[{"-", SuperscriptBox[ RowBox[{"(", RowBox[{"x", "-", SubscriptBox["x", "0"]}], ")"}], "2"]}], "/", RowBox[{"(", RowBox[{"2", " ", SuperscriptBox["a", "2"]}], ")"}]}]]}]}], TraditionalForm]], "InlineMath"], ", ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ OverscriptBox["\[Psi]", "~"], "(", "p", ")"}], "=", RowBox[{ FractionBox["1", SqrtBox[ RowBox[{"2", " ", "\[Pi]", " ", "\[HBar]"}]]], RowBox[{ SubsuperscriptBox["\[Integral]", RowBox[{"-", "\[Infinity]"}], "\[Infinity]"], RowBox[{ RowBox[{"\[Psi]", "(", "x", ")"}], " ", SuperscriptBox["e", RowBox[{"\[ImaginaryI]", " ", "p", " ", "x"}]], "d", "\[InvisibleSpace]", "x"}]}]}]}], TraditionalForm]], "InlineMath"], " in the position and momentum representations, respectively. The top-left \ panel shows the position-space probability density ", Cell[BoxData[ FormBox[ RowBox[{"\[RightBracketingBar]", RowBox[{"\[Psi]", "(", "x", ")"}], SuperscriptBox["\[LeftBracketingBar]", "2"]}], TraditionalForm]], "InlineMath"], ", position expectation value ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[LeftAngleBracket]", OverscriptBox["x", "^"], "\[RightAngleBracket]"}], "=", SubsuperscriptBox["\[Integral]", RowBox[{"-", "\[Infinity]"}], "\[Infinity]"]}], "\[RightBracketingBar]"}], RowBox[{"\[Psi]", "(", "x", ")"}], RowBox[{ SuperscriptBox["\[LeftBracketingBar]", "2"], " ", RowBox[{"x", " ", "d", "\[InvisibleSpace]", "x"}]}]}], TraditionalForm]], "InlineMath"], ", and position uncertainty ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"\[CapitalDelta]", " ", "x"}], "=", SqrtBox[ RowBox[{ RowBox[{"\[LeftAngleBracket]", SuperscriptBox[ OverscriptBox["x", "^"], "2"], "\[RightAngleBracket]"}], "-", SuperscriptBox[ RowBox[{"\[LeftAngleBracket]", OverscriptBox["x", "^"], "\[RightAngleBracket]"}], "2"]}]]}], TraditionalForm]], "InlineMath"], ". The top-right panel shows the momentum-space probabiity density ", Cell[BoxData[ FormBox[ RowBox[{"\[LeftBracketingBar]", " ", RowBox[{ RowBox[{ OverscriptBox["\[Psi]", "~"], "(", "p", ")"}], SuperscriptBox["\[LeftBracketingBar]", "2"]}]}], TraditionalForm]], "InlineMath"], ", momentum expectation value ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ RowBox[{ RowBox[{"\[LeftAngleBracket]", OverscriptBox["p", "^"], "\[RightAngleBracket]"}], "=", SubsuperscriptBox["\[Integral]", RowBox[{"-", "\[Infinity]"}], "\[Infinity]"]}], "\[RightBracketingBar]"}], RowBox[{ OverscriptBox["\[Psi]", "~"], "(", "p", ")"}], RowBox[{ SuperscriptBox["\[LeftBracketingBar]", "2"], " ", RowBox[{ RowBox[{"p", " ", "d", "\[InvisibleSpace]", "p"}], "=", RowBox[{ SubsuperscriptBox["\[Integral]", RowBox[{"-", "\[Infinity]"}], "\[Infinity]"], RowBox[{ RowBox[{ SuperscriptBox["\[Psi]", "*"], "(", "x", ")"}], RowBox[{"(", RowBox[{ RowBox[{"-", FractionBox["\[ImaginaryI]", "\[HBar]"]}], FractionBox["d", RowBox[{"d", " ", "x"}]]}], ")"}], " ", RowBox[{"\[Psi]", "(", "x", ")"}], " ", "d", "\[InvisibleSpace]", "x"}]}]}]}]}], TraditionalForm]], "InlineMath"], ", and momentum uncertainty ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"\[CapitalDelta]", " ", "p"}], "=", SqrtBox[ RowBox[{ RowBox[{"\[LeftAngleBracket]", SuperscriptBox[ OverscriptBox["p", "^"], "2"], "\[RightAngleBracket]"}], "-", SuperscriptBox[ RowBox[{"\[LeftAngleBracket]", OverscriptBox["p", "^"], "\[RightAngleBracket]"}], "2"]}]]}], TraditionalForm]], "InlineMath"], ". The lower two panels show the complex wavepackets, where the shape is its \ modulus and the coloring represents the argument (the range ", Cell[BoxData[ FormBox["0", TraditionalForm]], "InlineMath"], " to ", Cell[BoxData[ FormBox[ RowBox[{"2", " ", "\[Pi]"}], TraditionalForm]], "InlineMath"], " corresponding to colors from red to magenta)." }], "ManipulateCaption"], Cell["THINGS TO TRY", "ManipulateCaption", FontSize->10, FontSlant->"Plain", FontColor->RGBColor[ 0.6950942244602121, 0.7903257801174944, 0.29706263828488594`], CellTags->"ControlSuggestions"], Cell[TextData[{ Cell[BoxData[ TooltipBox[ PaneSelectorBox[{False->Cell[TextData[StyleBox["Resize Images", FontFamily->"Verdana"]]], True->Cell[TextData[StyleBox["Resize Images", FontFamily->"Verdana", FontColor->GrayLevel[0.5]]]]}, Dynamic[ CurrentValue["MouseOver"]]], "\"Click inside an image to reveal its orange resize frame.\\nDrag any of \ the orange resize handles to resize the image.\"", LabelStyle->{ FontFamily -> "Verdana", FontSize -> 10, FontColor -> GrayLevel[0.35], Background -> GrayLevel[0.98]}]]], StyleBox["\[NonBreakingSpace]\[FilledVerySmallSquare]\[NonBreakingSpace]", FontColor->RGBColor[0.928786, 0.43122, 0.104662]], Cell[BoxData[ TooltipBox[ PaneSelectorBox[{False->Cell[TextData[StyleBox["Gamepad Controls", FontFamily->"Verdana"]]], True->Cell[TextData[StyleBox["Gamepad Controls", FontFamily->"Verdana", FontColor->GrayLevel[0.5]]]]}, Dynamic[ CurrentValue["MouseOver"]]], "\"Control this Demonstration with a gamepad or other\\nhuman interface \ device connected to your computer.\"", LabelStyle->{ FontFamily -> "Verdana", FontSize -> 10, FontColor -> GrayLevel[0.35], Background -> GrayLevel[0.98]}]]] }], "ManipulateCaption", CellMargins->{{Inherited, Inherited}, {0, 0}}, Deployed->True, FontFamily->"Verdana", CellTags->"ControlSuggestions"], Cell["RELATED LINKS", "RelatedLinksSection"], Cell[TextData[{ ButtonBox["Expectation Value", BaseStyle->"Hyperlink", ButtonData->{ URL["http://mathworld.wolfram.com/ExpectationValue.html"], None}, ButtonNote->"http://mathworld.wolfram.com/ExpectationValue.html"], " (", ButtonBox["Wolfram", BaseStyle->"SiteLink", ButtonData->{ URL["http://mathworld.wolfram.com/"], None}, ButtonNote->"http://mathworld.wolfram.com/"], " ", StyleBox[ButtonBox["MathWorld", BaseStyle->"SiteLink", ButtonData->{ URL["http://mathworld.wolfram.com/"], None}, ButtonNote->"http://mathworld.wolfram.com/"], FontSlant->"Italic"], ")" }], "RelatedLinks", CellID->40415622], Cell[TextData[{ ButtonBox["Probability Density Function", BaseStyle->"Hyperlink", ButtonData->{ URL["http://mathworld.wolfram.com/ProbabilityDensityFunction.html"], None}, ButtonNote-> "http://mathworld.wolfram.com/ProbabilityDensityFunction.html"], " (", ButtonBox["Wolfram", BaseStyle->"SiteLink", ButtonData->{ URL["http://mathworld.wolfram.com/"], None}, ButtonNote->"http://mathworld.wolfram.com/"], " ", StyleBox[ButtonBox["MathWorld", BaseStyle->"SiteLink", ButtonData->{ URL["http://mathworld.wolfram.com/"], None}, ButtonNote->"http://mathworld.wolfram.com/"], FontSlant->"Italic"], ")" }], "RelatedLinks", CellID->1516799], Cell[TextData[{ ButtonBox["Uncertainty Principle", BaseStyle->"Hyperlink", ButtonData->{ URL["http://scienceworld.wolfram.com/physics/UncertaintyPrinciple.html"], None}, ButtonNote-> "http://scienceworld.wolfram.com/physics/UncertaintyPrinciple.html"], " (", StyleBox[ButtonBox["ScienceWorld", BaseStyle->"SiteLink", ButtonData->{ URL["http://scienceworld.wolfram.com/"], None}, ButtonNote->"http://scienceworld.wolfram.com/"], FontSlant->"Italic"], ")" }], "RelatedLinks", CellID->14787314], Cell[TextData[StyleBox[ButtonBox["DOWNLOAD DEMONSTRATION SOURCE CODE \ \[RightGuillemet]", BaseStyle->"Hyperlink", ButtonData->{ URL["http://demonstrations.wolfram.com/versions/source.jsp?id=\ ProbabilityDensitiesExpectationValuesAndUncertaintiesForGaus&version=0005"], None}, ButtonNote-> "http://demonstrations.wolfram.com/\ ProbabilityDensitiesExpectationValuesAndUncertaintiesForGaus/\ ProbabilityDensitiesExpectationValuesAndUncertaintiesForGaus-source.nb"], FontWeight->"Bold", FontColor->RGBColor[0.928786, 0.43122, 0.104662]]], "ShowSource", FontSize->10], Cell["PERMANENT CITATION DATA", "CitationSection"], Cell[TextData[{ "\"", ButtonBox["Probability Densities, Expectation Values, and Uncertainties for \ Gaussian Wavepackets", BaseStyle->"SiteLink", ButtonData->{ URL["http://demonstrations.wolfram.com/\ ProbabilityDensitiesExpectationValuesAndUncertaintiesForGaus/"], None}, ButtonNote-> "http://demonstrations.wolfram.com/\ ProbabilityDensitiesExpectationValuesAndUncertaintiesForGaus/"], "\"", " from ", ButtonBox["The Wolfram Demonstrations Project", BaseStyle->"SiteLink", ButtonData->{ URL["http://demonstrations.wolfram.com/"], None}, ButtonNote->"http://demonstrations.wolfram.com/"], "\[ParagraphSeparator]\[NonBreakingSpace]", ButtonBox["http://demonstrations.wolfram.com/\ ProbabilityDensitiesExpectationValuesAndUncertaintiesForGaus/", BaseStyle->"SiteLink", ButtonData->{ URL["http://demonstrations.wolfram.com/\ ProbabilityDensitiesExpectationValuesAndUncertaintiesForGaus/"], None}, ButtonNote-> "http://demonstrations.wolfram.com/\ ProbabilityDensitiesExpectationValuesAndUncertaintiesForGaus/"] }], "Citations"], Cell[" ", "AuthorSection"], Cell[TextData[{ "Contributed by: ", ButtonBox["Porscha McRobbie", BaseStyle->"Hyperlink", ButtonData->{ URL["http://demonstrations.wolfram.com/author.html?author=Porscha+\ McRobbie"], None}, ButtonNote-> "http://demonstrations.wolfram.com/author.html?author=Porscha+McRobbie"], " and ", ButtonBox["Eitan Geva", BaseStyle->"Hyperlink", ButtonData->{ URL["http://demonstrations.wolfram.com/author.html?author=Eitan+Geva"], None}, ButtonNote-> "http://demonstrations.wolfram.com/author.html?author=Eitan+Geva"] }], "Author", FontColor->GrayLevel[0.6], CellID->141335816], Cell[TextData[{ "\[Copyright] ", StyleBox[ButtonBox["The Wolfram Demonstrations Project & Contributors", BaseStyle->"Hyperlink", ButtonData->{ URL["http://demonstrations.wolfram.com/"], None}, ButtonNote->"http://demonstrations.wolfram.com/"], FontColor->GrayLevel[0.6]], "\[ThickSpace]\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]\ \[ThickSpace]", StyleBox[ButtonBox["Terms of Use", BaseStyle->"Hyperlink", ButtonData->{ URL["http://demonstrations.wolfram.com/termsofuse.html"], None}, ButtonNote->"http://demonstrations.wolfram.com/termsofuse.html"], FontColor->GrayLevel[0.6]] }], "Text", CellFrame->{{0, 0}, {0, 0.5}}, CellMargins->{{48, 48}, {20, 50}}, CellFrameColor->GrayLevel[0.45098], FontFamily->"Verdana", FontSize->9, FontColor->GrayLevel[0.6], CellTags->"Copyright"] }, Editable->False, Saveable->False, ScreenStyleEnvironment->"Working", CellGrouping->Manual, WindowSize->{750, 650}, WindowMargins->{{0, Automatic}, {Automatic, 0}}, WindowElements->{ "StatusArea", "MemoryMonitor", "MagnificationPopUp", "VerticalScrollBar", "MenuBar"}, WindowTitle->"Probability Densities, Expectation Values, and Uncertainties \ for Gaussian Wavepackets", DockedCells->{}, CellContext->Notebook, FrontEndVersion->"7.0 for Microsoft Windows (32-bit) (February 18, 2009)", StyleDefinitions->Notebook[{ Cell[ CellGroupData[{ Cell[ "Demonstration Styles", "Title", CellChangeTimes -> { 3.3509184553711*^9, {3.36928902713192*^9, 3.36928902738193*^9}, { 3.3754479092466917`*^9, 3.3754479095123196`*^9}, { 3.375558447161495*^9, 3.375558447395873*^9}, {3.37572892702972*^9, 3.375728927639103*^9}}], Cell[ StyleData[StyleDefinitions -> "Default.nb"]], Cell[ CellGroupData[{ Cell[ "Style Environment Names", "Section", CellChangeTimes -> {{3.369277974278112*^9, 3.369277974396138*^9}}], Cell[ StyleData[All, "Working"], ShowCellBracket -> False]}, Closed]], Cell[ CellGroupData[{ Cell[ "Notebook Options", "Section", CellChangeTimes -> {{3.374865264950812*^9, 3.374865265419568*^9}}], Cell[ " The options defined for the style below will be used at the \ Notebook level. ", "Text"], Cell[ StyleData["Notebook"], Editable -> True, PageHeaders -> {{None, None, None}, {None, None, None}}, PageFooters -> {{None, None, None}, {None, None, None}}, PageHeaderLines -> {False, False}, PageFooterLines -> {False, False}, PrintingOptions -> { "FacingPages" -> False, "FirstPageFooter" -> False, "RestPagesFooter" -> False}, CellFrameLabelMargins -> 6, DefaultNewInlineCellStyle -> "InlineMath", DefaultInlineFormatType -> "DefaultTextInlineFormatType", ShowStringCharacters -> True, CacheGraphics -> False, StyleMenuListing -> None, DemonstrationSite`Private`CreateCellID -> True, DemonstrationSite`Private`TrackCellChangeTimes -> False]}, Closed]], Cell[ CellGroupData[{ Cell[ "Input/Output", "Section", CellChangeTimes -> {{3.3756313297791014`*^9, 3.3756313299509783`*^9}}], Cell[ "The cells in this section define styles used for input and output \ to the kernel. Be careful when modifying, renaming, or removing these \ styles, because the front end associates special meanings with these style \ names. ", "Text"], Cell[ StyleData["Input"], CellMargins -> {{48, 4}, {6, 4}}], Cell[ StyleData["Output"], CellMargins -> {{48, 4}, {6, 4}}], Cell[ StyleData["DemonstrationHeader"], Deletable -> False, CellFrame -> {{0, 0}, {0, 1}}, ShowCellBracket -> False, CellMargins -> {{0, 0}, {30, 0}}, CellGroupingRules -> {"SectionGrouping", 20}, CellHorizontalScrolling -> True, CellFrameMargins -> {{0, 0}, {0, 0}}, CellFrameColor -> RGBColor[0.6449835965514611, 0.758632791638056, 0.2516823071641108], StyleMenuListing -> None, Background -> RGBColor[ 0.6449835965514611, 0.758632791638056, 0.2516823071641108]], Cell[ StyleData["ShowSource"], CellFrame -> {{0, 0}, {0, 1}}, ShowCellBracket -> False, CellMargins -> {{48, 48}, {8, 28}}, CellFrameMargins -> {{48, 48}, {6, 8}}, CellFrameColor -> RGBColor[0.691905, 0.790311, 0.300252], StyleMenuListing -> None, FontFamily -> "Helvetica", FontSize -> 10, FontWeight -> "Bold", FontSlant -> "Plain", FontColor -> RGBColor[1, 0.42, 0]]}, Closed]], Cell[ CellGroupData[{ Cell[ "Basic Styles", "Section", CellChangeTimes -> {{3.34971724802035*^9, 3.34971724966638*^9}, { 3.35091840608065*^9, 3.35091840781999*^9}, {3.35091845122987*^9, 3.35091845356607*^9}, {3.35686681885432*^9, 3.35686681945788*^9}, { 3.375657418186455*^9, 3.375657418452083*^9}}], Cell[ StyleData["Hyperlink"], StyleMenuListing -> None, FontColor -> GrayLevel[0]], Cell[ StyleData["SiteLink"], StyleMenuListing -> None, ButtonStyleMenuListing -> Automatic, FontColor -> GrayLevel[0.45098], ButtonBoxOptions -> { Active -> True, Appearance -> {Automatic, None}, ButtonFunction :> (FrontEndExecute[{ NotebookLocate[#2]}]& ), ButtonNote -> ButtonData}], Cell[ StyleData["Link"], FontColor -> GrayLevel[0.45098]], Cell[ CellGroupData[{ Cell[ StyleData["DemoNotes"], CellFrame -> True, CellMargins -> {{0, 0}, {0, 0}}, CellFrameMargins -> {{48, 48}, {4, 4}}, CellFrameColor -> GrayLevel[0.99], StyleMenuListing -> None, DemonstrationSite`Private`ReturnCreatesNewCell -> True, FontFamily -> "Verdana", FontSize -> 10, FontColor -> GrayLevel[0.45098]], Cell[ StyleData["DemoNotes", "Printout"], CellMargins -> {{24, 0}, {0, 10}}, FontSize -> 9]}, Closed]], Cell[ StyleData["SnapshotsSection"], CellFrame -> {{0, 0}, {0, 2}}, ShowCellBracket -> False, ShowGroupOpener -> True, CellMargins -> {{48, 48}, {10, 30}}, PrivateCellOptions -> {"DefaultCellGroupOpen" -> False}, CellGroupingRules -> {"SectionGrouping", 30}, CellFrameMargins -> {{8, 8}, {8, 2}}, CellFrameColor -> RGBColor[0.870588, 0.521569, 0.121569], DefaultNewCellStyle -> "SnapshotCaption", StyleMenuListing -> None, FontFamily -> "Verdana", FontSize -> 12, FontColor -> GrayLevel[0.45098]], Cell[ StyleData[ "SnapshotCaption", StyleDefinitions -> StyleData["DemoNotes"]], ShowCellBracket -> False], Cell[ CellGroupData[{ Cell[ StyleData["SnapshotOutput"], ShowCellBracket -> False, CellMargins -> {{48, 10}, {5, 7}}, Evaluatable -> True, CellGroupingRules -> "InputGrouping", PageBreakWithin -> False, GroupPageBreakWithin -> False, DefaultFormatType -> DefaultInputFormatType, ShowAutoStyles -> True, "TwoByteSyntaxCharacterAutoReplacement" -> True, HyphenationOptions -> { "HyphenationCharacter" -> "\[Continuation]"}, AutoItalicWords -> {}, LanguageCategory -> "Mathematica", FormatType -> InputForm, NumberMarks -> True, LinebreakAdjustments -> {0.85, 2, 10, 0, 1}, CounterIncrements -> "Input", DemonstrationSite`Private`StripStyleOnPaste -> True, DemonstrationSite`Private`MenuPosition -> 1500, DemonstrationSite`Private`MenuCommandKey -> "9"], Cell[ StyleData["SnapshotOuput", "Printout"], CellMargins -> {{39, 0}, {4, 6}}, LinebreakAdjustments -> {0.85, 2, 10, 1, 1}]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["DemoTitle"], Deletable -> False, ShowCellBracket -> False, CellMargins -> {{48, 48}, {22, 10}}, CellGroupingRules -> {"SectionGrouping", 20}, StyleMenuListing -> None, FontFamily -> "Verdana", FontSize -> 20, FontWeight -> "Bold", Background -> GrayLevel[1]], Cell[ StyleData["DemoName", "Printout"], CellMargins -> {{24, 8}, {8, 27}}, HyphenationOptions -> {"HyphenationCharacter" -> "-"}, FontSize -> 16]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["DetailsSection"], CellFrame -> {{0, 0}, {0, 1}}, ShowCellBracket -> False, CellMargins -> {{48, 48}, {8, 28}}, CellGroupingRules -> {"SectionGrouping", 25}, CellFrameMargins -> {{48, 48}, {6, 8}}, CellFrameColor -> RGBColor[0.691905, 0.790311, 0.300252], StyleMenuListing -> None, FontFamily -> "Helvetica", FontSize -> 10, FontWeight -> "Bold", FontColor -> RGBColor[0.691905, 0.790311, 0.300252]], Cell[ StyleData["DetailsSection", "Printout"], CellMargins -> {{12, 0}, {0, 16}}, PageBreakBelow -> False, FontSize -> 12]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["DemoSection"], CellFrame -> {{0, 0}, {0, 1}}, ShowCellBracket -> False, CellMargins -> {{48, 48}, {8, 28}}, CellGroupingRules -> {"SectionGrouping", 30}, CellFrameMargins -> {{48, 48}, {6, 8}}, CellFrameColor -> RGBColor[ 0.6950942244602121, 0.7903257801174944, 0.29706263828488594`], StyleMenuListing -> None, FontFamily -> "Helvetica", FontSize -> 10, FontWeight -> "Bold", FontSlant -> "Plain", FontColor -> RGBColor[ 0.6950942244602121, 0.7903257801174944, 0.29706263828488594`]], Cell[ StyleData["DemoSection", "Printout"], CellMargins -> {{12, 0}, {0, 16}}, PageBreakBelow -> False, FontSize -> 12]}, Closed]], Cell[ StyleData["ManipulateSection"], CellFrame -> {{0, 0}, {0, 2}}, ShowCellBracket -> False, CellMargins -> {{48, 48}, {10, 30}}, CellGroupingRules -> {"SectionGrouping", 30}, CellFrameMargins -> {{8, 8}, {8, 2}}, CellFrameColor -> RGBColor[0.870588, 0.521569, 0.121569], StyleMenuListing -> None, FontFamily -> "Verdana", FontSize -> 12], Cell[ StyleData["ManipulateCaptionSection"], CellFrame -> {{0, 0}, {0, 2}}, ShowCellBracket -> False, CellMargins -> {{48, 48}, {10, 30}}, CellGroupingRules -> {"SectionGrouping", 30}, CellFrameMargins -> {{8, 8}, {8, 2}}, CellFrameColor -> RGBColor[0.870588, 0.521569, 0.121569], DefaultNewCellStyle -> "ManipulateCaption", StyleMenuListing -> None, FontFamily -> "Verdana", FontSize -> 12, FontColor -> GrayLevel[0.45098]], Cell[ StyleData["ManipulateCaption"], ShowCellBracket -> False, CellMargins -> {{48, 48}, {10, 16}}, StyleMenuListing -> None, DemonstrationSite`Private`ReturnCreatesNewCell -> True, FontFamily -> "Verdana", FontSize -> 11, FontColor -> GrayLevel[0]], Cell[ StyleData[ "SeeAlsoSection", StyleDefinitions -> StyleData["DemoSection"]], ShowCellBracket -> False, DefaultNewCellStyle -> "SeeAlso"], Cell[ StyleData["SeeAlso", StyleDefinitions -> StyleData["DemoNotes"]], CellDingbat -> Cell["\[FilledSmallSquare]", FontColor -> RGBColor[0.928786, 0.43122, 0.104662]], ShowCellBracket -> False, FontColor -> GrayLevel[0.45098]], Cell[ StyleData[ "RelatedLinksSection", StyleDefinitions -> StyleData["DemoSection"]], ShowCellBracket -> False, DefaultNewCellStyle -> "RelatedLinks"], Cell[ StyleData[ "RelatedLinks", StyleDefinitions -> StyleData["DemoNotes"]], CellDingbat -> Cell["\[FilledSmallSquare]", FontColor -> RGBColor[0.928786, 0.43122, 0.104662]], ShowCellBracket -> False, FontColor -> GrayLevel[0.45098]], Cell[ StyleData[ "CategoriesSection", StyleDefinitions -> StyleData["DemoSection"]], ShowCellBracket -> False, DefaultNewCellStyle -> "Categories"], Cell[ StyleData["Categories", StyleDefinitions -> StyleData["DemoNotes"]], ShowCellBracket -> False], Cell[ StyleData[ "AuthorSection", StyleDefinitions -> StyleData["DemoSection"]], ShowCellBracket -> False, CellMargins -> {{48, 48}, {4, 18}}, CellElementSpacings -> {"CellMinHeight" -> 3}, CellFrameMargins -> {{48, 48}, {6, 3}}, DefaultNewCellStyle -> "Author", FontSize -> 1, FontColor -> GrayLevel[1]], Cell[ StyleData["Author", StyleDefinitions -> StyleData["DemoNotes"]], CellDingbat -> Cell["\[FilledSmallSquare]", FontColor -> GrayLevel[0.64]], ShowCellBracket -> False], Cell[ StyleData[ "DetailNotes", StyleDefinitions -> StyleData["DemoNotes"]], ShowCellBracket -> False, FontColor -> GrayLevel[0]], Cell[ StyleData[ "CitationSection", StyleDefinitions -> StyleData["DemoSection"]], ShowCellBracket -> False, CellMargins -> {{48, 48}, {8, 14}}, DefaultNewCellStyle -> "Categories"], Cell[ StyleData["Citations", StyleDefinitions -> StyleData["DemoNotes"]], ShowCellBracket -> False, ParagraphSpacing -> {0, 6}], Cell[ StyleData[ "RevisionSection", StyleDefinitions -> StyleData["DemoSection"]], DefaultNewCellStyle -> "RevisionNotes"], Cell[ StyleData[ "RevisionNotes", StyleDefinitions -> StyleData["DemoNotes"]], ShowCellBracket -> False]}, Closed]], Cell[ CellGroupData[{ Cell[ "Specific Styles", "Section", CellChangeTimes -> {{3.34971724802035*^9, 3.34971724966638*^9}, { 3.35091840608065*^9, 3.35091840781999*^9}, {3.35091845122987*^9, 3.35091845356607*^9}, {3.36230868322317*^9, 3.36230868335672*^9}, { 3.36928857618576*^9, 3.36928857640452*^9}, {3.3737586217185173`*^9, 3.373758622077897*^9}}], Cell[ StyleData["InitializationSection"], CellFrame -> {{0, 0}, {0, 2}}, ShowCellBracket -> False, CellMargins -> {{48, 48}, {10, 30}}, CellGroupingRules -> {"SectionGrouping", 30}, CellFrameMargins -> {{8, 8}, {8, 2}}, CellFrameColor -> RGBColor[0.870588, 0.521569, 0.121569], StyleMenuListing -> None, FontFamily -> "Verdana", FontSize -> 12, FontColor -> GrayLevel[0.45098]], Cell[ CellGroupData[{ Cell[ StyleData["AnchorBar"], ShowCellBracket -> False, CellMargins -> {{48, 44}, {3, 6}}, StyleMenuListing -> None, FontFamily -> "Verdana", FontSize -> 9, FontColor -> GrayLevel[0.5]], Cell[ StyleData["AnchorBar", "Presentation"], FontSize -> 18], Cell[ StyleData["AnchorBar", "SlideShow"], StyleMenuListing -> None], Cell[ StyleData["AnchorBar", "Printout"], FontSize -> 9]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["AnchorLink"], StyleMenuListing -> None, ButtonStyleMenuListing -> Automatic, FontColor -> RGBColor[0.5, 0.5, 0.5], ButtonBoxOptions -> { Active -> True, ButtonFunction :> (FrontEndExecute[{ FrontEnd`NotebookLocate[#2]}]& ), ButtonNote -> ButtonData}], Cell[ StyleData["AnchorLink", "Printout"], FontVariations -> {"Underline" -> False}, FontColor -> GrayLevel[0]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["GamePadStatus"], ShowCellBracket -> False, CellMargins -> {{48, 48}, {5, 5}}, StyleMenuListing -> None, FontFamily -> "Verdana", FontSize -> 10], Cell[ StyleData["GamePadStatus", "Printout"], CellMargins -> {{24, 0}, {0, 10}}, FontSize -> 9]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["DemoInstruction"], CellMargins -> {{48, 48}, {5, 5}}, CellFrameLabelMargins -> 2, StyleMenuListing -> None, DemonstrationSite`Private`ReturnCreatesNewCell -> True, DemonstrationSite`Private`MenuPosition -> 800, DemonstrationSite`Private`MenuCommandKey -> "8", FontFamily -> "Verdana", FontSize -> 11, Background -> RGBColor[1, 0.85, 0.5]], Cell[ StyleData["DemoInstruction", "Printout"], CellMargins -> {{24, 0}, {0, 10}}, Hyphenation -> True, HyphenationOptions -> {"HyphenationCharacter" -> "-"}, LineSpacing -> {1., 2, 2.}, FontSize -> 9]}, Closed]], Cell[ StyleData[ "ImplementationSection", StyleDefinitions -> StyleData["DemoSection"]], Deletable -> True, DefaultNewCellStyle -> "ImplementationNotes"], Cell[ StyleData[ "ImplementationNotes", StyleDefinitions -> StyleData["DemoNotes"]]], Cell[ StyleData[ "StatusSection", StyleDefinitions -> StyleData["DemoSection"]], DefaultNewCellStyle -> "StatusNotes"], Cell[ StyleData[ "StatusNotes", StyleDefinitions -> StyleData["DemoNotes"]]], Cell[ CellGroupData[{ Cell[ StyleData["SectionGloss"], StyleMenuListing -> None, FontSize -> 0.85 Inherited, FontWeight -> "Plain", FontColor -> GrayLevel[0.6]], Cell[ StyleData["SectionGloss", "Printout"]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["InlineFormula"], "TwoByteSyntaxCharacterAutoReplacement" -> True, HyphenationOptions -> { "HyphenationCharacter" -> "\[Continuation]"}, LanguageCategory -> "Formula", AutoSpacing -> True, ScriptLevel -> 1, AutoMultiplicationSymbol -> False, SingleLetterItalics -> False, SpanMaxSize -> 1, StyleMenuListing -> None, FontFamily -> "Courier", FontSize -> 1.05 Inherited, ButtonBoxOptions -> {Appearance -> {Automatic, None}}, FractionBoxOptions -> {BaseStyle -> {SpanMaxSize -> Automatic}}, GridBoxOptions -> { GridBoxItemSize -> { "Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}}], Cell[ StyleData["InlineFormula", "Printout"], CellMargins -> {{2, 0}, {0, 8}}]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["InlineOutput"], CellHorizontalScrolling -> True, "TwoByteSyntaxCharacterAutoReplacement" -> True, HyphenationOptions -> { "HyphenationCharacter" -> "\[Continuation]"}, LanguageCategory -> None, AutoMultiplicationSymbol -> False, StyleMenuListing -> None, FontFamily -> "Courier", FontSize -> 1.05 Inherited], Cell[ StyleData["InlineOutput", "Printout"], CellMargins -> {{2, 0}, {0, 8}}]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["InlineMath"], DefaultFormatType -> "DefaultTextFormatType", DefaultInlineFormatType -> "TraditionalForm", LanguageCategory -> "Formula", AutoSpacing -> True, ScriptLevel -> 1, AutoMultiplicationSymbol -> False, SingleLetterItalics -> True, SpanMaxSize -> DirectedInfinity[1], StyleMenuListing -> None, FontFamily -> "Times", FontSize -> 1.05 Inherited, ButtonBoxOptions -> {Appearance -> {Automatic, None}}, GridBoxOptions -> { GridBoxItemSize -> { "Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}}], Cell[ StyleData["InlineMath", "Printout"], CellMargins -> {{2, 0}, {0, 8}}]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["TableBase"], CellMargins -> {{48, 48}, {4, 4}}, SpanMaxSize -> 1, StyleMenuListing -> None, FontFamily -> "Courier", FontSize -> 11, ButtonBoxOptions -> {Appearance -> {Automatic, None}}, GridBoxOptions -> { GridBoxAlignment -> { "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}}], Cell[ StyleData["TableBase", "Printout"], CellMargins -> {{2, 0}, {0, 8}}, FontSize -> 9]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData[ "1ColumnTableMod", StyleDefinitions -> StyleData["TableBase"]], GridBoxOptions -> {GridBoxItemSize -> {"Columns" -> { Scaled[0.04], { Scaled[0.966]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}, GridBoxSpacings -> {"Columns" -> { Offset[0.28], Offset[0.126], { Offset[0.77]}, Offset[0.28]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}}], Cell[ StyleData[ "1ColumnTableMod", "Printout", StyleDefinitions -> StyleData["TableBase", "Printout"]], GridBoxOptions -> {GridBoxItemSize -> {"Columns" -> { Scaled[0.078], { Scaled[0.922]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}, GridBoxSpacings -> {"Columns" -> { Offset[0.28], { Offset[0.56]}, Offset[0.28]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.56]}, Offset[0.2]}, "RowsIndexed" -> {}}}]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData[ "2ColumnTableMod", StyleDefinitions -> StyleData["TableBase"]], GridBoxOptions -> {GridBoxItemSize -> {"Columns" -> { Scaled[0.05], Scaled[0.41], { Scaled[0.565]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}, GridBoxSpacings -> {"Columns" -> { Offset[0.28], Offset[0.14], { Offset[0.77]}, Offset[0.28]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}}], Cell[ StyleData[ "2ColumnTableMod", "Printout", StyleDefinitions -> StyleData["TableBase", "Printout"]], GridBoxOptions -> {GridBoxItemSize -> {"Columns" -> { Scaled[0.079], Scaled[0.363], { Scaled[0.558]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}, GridBoxSpacings -> {"Columns" -> { Offset[0.28], { Offset[0.56]}, Offset[0.28]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.56]}, Offset[0.2]}, "RowsIndexed" -> {}}}]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData[ "3ColumnTableMod", StyleDefinitions -> StyleData["TableBase"]], GridBoxOptions -> {GridBoxItemSize -> {"Columns" -> { Scaled[0.04], Scaled[0.266], Scaled[0.26], { Scaled[0.44]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}, GridBoxSpacings -> {"Columns" -> { Offset[0.28], Offset[0.14], { Offset[0.77]}, Offset[0.28]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}}], Cell[ StyleData[ "3ColumnTableMod", "Printout", StyleDefinitions -> StyleData["TableBase", "Printout"]], GridBoxOptions -> {GridBoxItemSize -> {"Columns" -> { Scaled[0.08], Scaled[0.25], Scaled[0.25], { Scaled[0.42]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}, GridBoxSpacings -> {"Columns" -> { Offset[0.28], { Offset[0.56]}, Offset[0.28]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.56]}, Offset[0.2]}, "RowsIndexed" -> {}}}]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["TableText"], Deletable -> False, StyleMenuListing -> None, FontFamily -> "Verdana", FontSize -> 0.952 Inherited], Cell[ StyleData["TableText", "Printout"], CellMargins -> {{24, 0}, {0, 8}}, Hyphenation -> True, HyphenationOptions -> {"HyphenationCharacter" -> "-"}, LineSpacing -> {1., 2, 2.}]}, Closed]], Cell[ StyleData["Continuation"], FontColor -> GrayLevel[1]]}, Closed]]}, Open]]}, Visible -> False, FrontEndVersion -> "7.0 for Microsoft Windows (32-bit) (February 18, 2009)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{ "ControlSuggestions"->{ Cell[119340, 2453, 198, 5, 70, "ManipulateCaption", CellTags->"ControlSuggestions"], Cell[119541, 2460, 1368, 31, 70, "ManipulateCaption", CellTags->"ControlSuggestions"]}, "Copyright"->{ Cell[125149, 2631, 822, 23, 70, "Text", CellTags->"Copyright"]} } *) (*CellTagsIndex CellTagsIndex->{ {"ControlSuggestions", 152434, 3213}, {"Copyright", 152633, 3218} } *) (*NotebookFileOutline Notebook[{ Cell[646, 22, 24340, 401, 70, "DemonstrationHeader"], Cell[24989, 425, 116, 3, 70, "DemoTitle"], Cell[25108, 430, 89278, 1870, 70, "Output", CellID->512058499], Cell[114389, 2302, 4948, 149, 70, "ManipulateCaption"], Cell[119340, 2453, 198, 5, 70, "ManipulateCaption", CellTags->"ControlSuggestions"], Cell[119541, 2460, 1368, 31, 70, "ManipulateCaption", CellTags->"ControlSuggestions"], Cell[120912, 2493, 44, 0, 70, "RelatedLinksSection"], Cell[120959, 2495, 640, 21, 70, "RelatedLinks", CellID->40415622], Cell[121602, 2518, 674, 22, 70, "RelatedLinks", CellID->1516799], Cell[122279, 2542, 526, 17, 70, "RelatedLinks", CellID->14787314], Cell[122808, 2561, 578, 13, 70, "ShowSource"], Cell[123389, 2576, 50, 0, 70, "CitationSection"], Cell[123442, 2578, 1068, 28, 70, "Citations"], Cell[124513, 2608, 26, 0, 70, "AuthorSection"], Cell[124542, 2610, 604, 19, 70, "Author", CellID->141335816], Cell[125149, 2631, 822, 23, 70, "Text", CellTags->"Copyright"] } ] *) (* End of internal cache information *) (* NotebookSignature JRUzjAZHw3t7jum2Sa@42fHF *)