{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Numerical methods for the Schrodinger equation\n", "\n", "##### by Justin Cai and Sam Bateman" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "from tise_code import *" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solving the time-independent Schrodinger equation\n", "\n", "Recall the that time-independent Schrodinger equation (TISE) is \n", "\n", "$$-\\frac{\\hbar^2}{2m}\\frac{d^2\\psi}{dx^2} + V \\psi = E\\psi.$$\n", "\n", "When solving the time-independet Schrodinger equation (TISE), we are faced with solving a boundary value problem (BVP), or finding a solution to a differential equation with the solution being specified at two or more points. This is contrasted with an initial value problem (IVP), where we want to find a solution with the solution only specified at one point. For the TISE, if we restrict our particle to the finite domain $[a, b]$, then we'll have that $\\psi(a)=0=\\psi(b)$ as our boundary conditions.\n", "\n", "### Shooting method\n", "\n", "One method to solving boundary value problems is called the shooting method. The shooting method turns the problem into an initial value problem by starting at one of the boundaries, guessing an initial free parameter, solving up to the boundary (that is, \"shooting\" to the boundary), and checking if our solution matches the boundary condition. If it does not, we update our guess on our free parameter and then repeat this process until our solution is sufficiently close to the boundary condition.\n", "\n", "Let's see this in a simple scenario with an infinite square well. Recall that the potential of an infinite square is \n", "\n", "$$V(x) = \\begin{cases}0 & 0 \\leq x \\leq L \\\\ \\infty & \\text{otherwise} \\end{cases},$$\n", "\n", "so we get the boundary conditions $\\psi(0)=0=\\psi(L)$ discussed earlier. We'll have to make a guess for the initial slope, so turning this into an IVP, we have $\\psi(0)=0, \\psi'(0)=s$, where $s$ is a free parameter. For arbitrary potentials, we also don't know $E$, the total energy of the system, but for now, we'll plug in the analytic solution for the energy of an infinite square well,\n", "\n", "$$E_n = \\frac{n^2 \\pi^2 \\hbar^2}{2mL^2}.$$\n", "\n", "For convenience, we'll also set $m=1$ and $h=1$ (so $\\hbar = \\frac{1}{2\\pi}$). If we solve this IVP with the correct energy, then we see that the initial slope doesn't really matter:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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aNYwbN46xY8cyZcoUYmJiTvvta2trueqqq8jMzGTJkiUN+hyvkFQPCkki4rgDG2DxH48udLdc0O9qGPkriD/D2dpEmoq7GjbMhBV/NU1JACI7mC8FBt6gNUsiJ9GSGzfYts2qVatYsGABs2fPJicnh/T0dFatWtXg6Xa1tbVcffXV7N69m88//5y4uLgG1aKQVA8KSSLimIJd8Pkj8M375tzygzOvhvN+BfHdnK1NpLl4auGr12HZX6Aky1yL6QyjfmsaPKgbnsgRLTkkHcvj8ZCWlsa9997LjBkzGjTd7nBA2rFjB4sXL6Zdu3YNfn81bhAR8UUl2WbN0fpXj3ar63eV+VCozTelrfELgMHTof9UWPcSLH8SDmXA7NthxVNwwX2mdbgalYi0WOnp6SxatIixY8eSkJBAeno6+fn59OrVi4iIiJOuNzoZt9vNlClTWL9+PfPmzcPj8ZCTkwNAbGwsgYGBTfmf8b0UkkRETlflIVjxtOny5a40184Ya7p/tT/T2dpEnBYQDMPugoHTYM2zZs1S/jZ450boOATGPgKpQ52uUkROQ2RkJMuWLePpp5+mpKSEtLQ0nnzyScaPH9+g19m/fz9z584FYMCAAcfdt3jxYkaNGtVYJTeYptuJiDSUuwbWPAfLHoeqYnMtZSiMfhA6DXe2NhFfVVlkOuGt/ufRhem9JsKYhzTiKm1Wa5lu57SmmG7nauQaRURaL9uGrR/CM0Ngwf0mICX0hqlvwS2fKiCJfJ+QaLjwfvj5V3DWjaahyda58MxQ+Ph/oaLQ6QpFRI5QSBIRqY8DG+DlS+HtG8z6ivBEmPhPuHMF9Biv9RUi9RWRZDalvXMldLsIvLWQ/m/42wAzJc9d7XSFIiIKSSIi36skGz64G54bBXtXgH+w6Vb3s3Vw1jR16hI5XYm94YZZMO0DSOwH1cWw8AH41zD49lOnqxORNk6NG0RETsZdbdZOLHsSasvNtX5Xw+gHIDrF2dpEWpOuF8AdS2HT2/DZw1C4G964Gs4YBxf/SeuVRMQRCkkiIt+1cxF8/Bso2GnOOw4xH9Y6Dna2LpHWyuUHA66DXpfB0sfhi3/Djk9h1+dwzk/MhrRB4U5XKSJtiKbbiYgcVrQP3p4Gr082ASksASY9B7cuUEASaQ5BETD2D3D3aug2xqxXWvk0/HMwbHrXNE8REWkGCkkiIu5qs+HlM0NMty3LD4bdDT9bC/2vUVMGkeYWfwZcP8t0jozpBKXZ8P5t8NJ4yNvqdHUi0gZoup2ItG27Pof5vz46tS71XLjkCUjs42xdIm2dZZnOkV0uMOsDlz8JmavhPyNg+P+YKXgBIU5XKSKtlEaSRKRtKsuH926D1yYdP7Vu+nwFJBFfEhAMI38FP1kDPS4Br9sEpn8NM+sHRUSagEKSiLQttg0b3oBnzobN75oNLYfeqal1Ir4uOgWmvgHXzITIDnBoj1k/OOtWKM11ujoRaWUUkkSk7SjYBa9eDh/cBZWHzN4st30G4/8MwVFOVyci9dHrUvhJulk3aLng61nwz7Nh7Yvg9TpdnYg0gueee45Ro0YRGRmJZVkUFRU1ew0KSSLS+nlqYflT8O9zIWOp2RB2zMNw+2LoMMjp6kSkoYIiTFv+GYuh/QCzEe28X8DLE+DgTqerE5EfqaKigosvvpj77rvPsRrUuEFEWres9TD355C72Zx3GQWX/hViuzhZlYg0huQBMONz+PJ5WPT7usYOw+GC+83+Si4/pysUaRDbtql0Vzry3iH+IVgNmHI+a9YsHn74YXbu3EloaCgDBw5kzpw5hIWF/eha7rnnHgCWLFnyo1/rdCkkiUjr5K6GJY+ZPVZsL4TEwrhHof+1Wnck0pq4/GDoHaYT3of/YzpWLvw/2PIBXP4MJPRyukKReqt0VzL0jaGOvHf6demEBoTW67HZ2dlMnTqVxx9/nEmTJlFaWsry5cuxbZuZM2dyxx13fO/zn332Wa6//vrGKLvJKCSJSOuTtR4+uBvy6/ZT6XsljH8cwuKdrUtEmk50KtzwPnz1Onx6P2Stg2dHwvm/geH3gF+A0xWKtBrZ2dm43W4mT55MWloaAP369QNg4sSJDB36/UEvMTGxyWv8sRSSRKT1cFfD0sdhxV/B9kBYOzO1rtdlTlcmIs3BsuCsadBtNHx4D+z4FD5/BLbMNaNK7c90ukKR7xXiH0L6demOvXd99e/fn9GjR9OvXz/GjRvH2LFjmTJlCjExMURERBAREVGv13n00Ud59NFHj5xv2bKF1NTUBtfeFCzbtp2uoVFZlhUJFBcXFxMZGel0OSLSXA5sMF3r8raY8z6TYcITEBbnbF0i4gzbhk3vwMe/gaoicPnD+f8PRtwLfvqOWHxDVVUVGRkZdO7cmeDgYKfLaRDbtlm1ahULFixg9uzZ5OTkkJ6ezqpVq+o93a6wsJDCwsIj1zt16oS//9G/n0uWLOGCCy7g0KFDREdHn/L1vu//Y0lJCVFRUQBRtm2X1Pe/T78lRKRlc9fA8idg2RNm9Cg0Di55Cvpc4XRlIuIkyzJ7n3UZBfN/CVs/hMV/hG8/hUnPQnw3pysUadEsy2L48OEMHz6cBx54gLS0NGbPns2MGTPqPd0uNjaW2NjY5ii3wRSSRKTlyv8W3r8Nsjea895XwCVPau2RiBwVkQhXv2ZGleb/GrLWwrPnwdg/wOBb1chF5DSkp6ezaNEixo4dS0JCAunp6eTn59OrV68GTbc7lZycHHJycti507T037x5MxEREaSmpjZbqNI+SSLS8ti2afn77EgTkEJiYMqLcPUrCkgicqLDo0p3r4LOI6G2Aj76JcycAiXZTlcn0uJERkaybNkyJkyYQPfu3fnd737Hk08+yfjx4xvl9f/zn/8wcOBAZsyYAcDIkSMZOHAgc+fObZTXrw+tSRKRlqUsD+b8BHYsMOddLoAr/gWRyc7WJSItg9cLa56Fzx4Cd5X5kuWSp6DvZKcrkzaoJa9J8iVNsSZJI0ki0nJs/xj+dY4JSH5BcPFjpuWvApKI1JfLBcPugtuXQvv+UHkIZk2H92ZAVbHT1YmIj1BIEhHfV1Nu2vm+eS1UHISEPnD7YvNBx6VfYyJyGhJ6wq2fwcjfgOUHm9+B/5wH+9c6XZmI+AB9uhAR35a13qw9WveSOT/npzDjc0js42xdItLy+QfChffDLZ+YzWiL9sKL42D5U2Zanoi0WQpJIuKbbBtWPwMvjIWCnRCRDDfOgXF/hADN2xaRRpQyBO5cYfZX87ph0cPw2hVq6iDShikkiYjvKS8wU+s+vQ+8tdDrMrhrpdnvRESkKQRHmS6ZE/8JAaGQsRT+M9zsqyTSxFpbI7Xm1hT//xSSRMS37F0F/xkB335imjNc8qTZ4yTUNzebE5FWxLLgrGmmqUNSP6gogDeuho//F9zVTlcnrZCfnx8ANTU1DlfSslVUVAAQEBDQaK+pFuAi4hu8HrMOYMmjYHshrhtc9bL5oCIi0tzc1bDwQUj/tzlP6gdTXob4bo6WJa2LbdtkZmZSW1tLcnIyLjUjahDbtqmoqCAvL4/o6Gjat29/wmNOtwW4QpKIOK80B96fARnLzHn/qTDhCQgKd7YuEZFvP4UP7jKjSoERcPk/oM8kp6uSVqSmpoaMjAy8ahZy2qKjo0lKSsKyrBPuU0iqo5Ak0sLsXASz74DyfAgIM9PrBkx1uioRkaNKsuG9W2HvSnM+5A4Y+4jpjifSCLxer6bcnaaAgIAj0xZPRiGpjkKSSAvh9cDSx2HpnwEbEvvClJegXXenKxMROZHHDYsfgRV/NecdBpkpwdGpjpYlIt/vdEOSJj6KSPMrL4CZV8HSxwAbBk2H2z5TQBIR3+XnD2MeguvegeBoyFpnNp/d/onTlYlIE1BIEpHmlbUOnjsfdi0C/xCY9Cxc9jQEhDhdmYjID+s+Du5cbkaSqorgzWtMgweP2+nKRKQRKSSJSPOwbfjyBXjxYijeB7FdYcYi6H+t05WJiDRMdCpM/8SsTQJY+TS8OlGbz4q0IgpJItL0aipg9p3w0b3gqYGel8LtiyGxj9OViYicHv9AmPC4WZcUGGGaOjx3Puxd7XRlItIIFJJEpGkV7ILnx8Cmt8Dyg4v+ANe8bna3FxFp6fpMgjuWQkJvKMuFVy6FNf81o+ci0mIpJIlI09k2H54bBXnfQFgC3DQXhv/c7GovItJaxHU1zWf6TAavG+b/Cj64G2orna5MRE6TQpKIND6vF5b8Gd6aCtUlkHquWejcaYTTlYmINI3AMJjyotk/yXLBxjfgxXFQlOl0ZSJyGhSSRKRxVZfCO9NgyaPmfMgdZgQpIsnZukREmpplwbk/g2mzISQWsjea0fTdS52uTEQaSCFJRBpPwS54/iLYNg/8AuHyZ8zCZr8ApysTEWk+XUaZdUrtB0BFAbx2Baz8u9YpibQgCkki0jh2fgb/vQDyt0JEe5j+MQy8wemqREScEZ0Kt3wCA64H2wsL/w9m3WK6fYqIz1NIEpEfx7Zh5d9g5lVQVQwdh8DtS6DjYKcrExFxVkBI3Yj6E+Dyh2/eh5cuhuIspysTkR+gkCQip6+mAt67DRY+YL4pPetGuHme1h+JiBxmWTBkBtz0IYTGmXVK/70A9q91ujIR+R4KSSJyeor2mc5NX88y35BOeAIu+zv4BzldmYiI70k7F2YshoQ+Zj+llybAxredrkpETkEhSUQabt+X8N8LIWcThMbDjXPNN6Xa/0hE5NRi0uDWT6HHBPBUw+zbYeGD4PU4XZmIfIdCkog0zOZZ8PIlUJ4Hif3M+qNOw52uSkSkZQiKgGtmwoh7zfnKp+Gt6832CSLiMxSSRKR+bBsWPwrv3Wq+Ae0xwXRuik5xujIRkZbF5YIxD8Lk58EvCL792GyfUJjhdGUiUkchSUR+WG0lzJoOS/9szs/9OVzzOgSFO1uXiEhLduZVZruE8CSzfcJ/L4Q9K5yuSkRQSBKRH1KaYxYYfzMbXAEw8Z8w9g/g8nO6MhGRlq/jILh9MSQPhMpCePVy+Gqm01WJtHkKSSJyatkbzTebB9ZDSAzc+AGcNc3pqkREWpfIZDOi1GcSeN0w5274/BEzzVlEHKGQJCInt3UevHgxlGRBfHe4bRF0GuF0VSIirVNACFz5Ipz3S3O+7C9mH7raKmfrEmmjFJJE5Hi2Dav+CW/fALUV0OUCuHUhxHV1ujIRkdbN5YLRD5hpzS5/sw/dq5dDeYHTlYm0Oc0SkizLutuyrAzLsqosy1pnWdZ59XzetZZl2ZZlfdDUNYoIZq+Oj38DC+4HbBh8C1z/LoREO12ZiEjbcdY0uOE9CIqCfV/A86Ph4E6nqxJpU5o8JFmWdQ3wNPBHYCCwHPjYsqzUH3heGvBE3eNFpKnVVMDb02DNc+Z87CNwyVPgF+BsXSIibVGXUXDrAohOhUMZJijtWel0VSJtRnOMJN0LvGDb9vO2bW+1bfseYB9w16meYFmWHzATeBDY3Qw1irRtZfnwyqWw/SOzZ8dVL8O5PwPLcroyEZG2K6GnWQ/aYTBUFZmpdxvfcroqkTahSUOSZVmBwCBgwXfuWgCc+z1PfQDIt237hXq8R5BlWZGHDyDitAsWaYsO7jDfUGatMx3sbpprOiyJiIjzwhPg5nnQ+wrw1sLsO2Dxn9T5TqSJNfVIUjzgB+R+53oukHSyJ1iWNRy4FZhRz/f4LVB8zLH/tCoVaYv2roYXLoKivRDTCW79DFKHOV2ViIgcKyAEprwEI35hzpc+BnN/Bh63s3WJtGLN1d3uu193WCe5hmVZEcDrwAzbtg/W87X/BEQdc3T8EXWKtB1fv2+mblQeMlM5bv0M4rs5XZWIiJyMywVjHoJLnwbLBV+9Bm9NhZpypysTaZWaOiQdBDycOGqUwImjSwBdgU7Ah5ZluS3LcgM3AhPrzk/oQWzbdrVt2yWHD6C0Uf8LRFob24aVf4NZ08FTDT0vhZs+hPB2TlcmIiI/ZPB0uGYm+IfAjgXw8qVmXamINKomDUm2bdcA64CLvnPXRcCqkzxlG9APGHDMMRdYXHd7X5MVK9IWeD0w/1ew8AFzPvROuPpVCAx1ti4REam/nhPMl1shsXBgPbw4FgrV50rdsKKNAAAgAElEQVSkMTXHdLungNssy7rFsqxelmX9FUgF/gNgWdarlmX9CcC27Srbtr8+9gCKgNK685pmqFekdaqtgndvgi+fBywY9ycY/2dw+TldmYiINFTK2UdbhBfuhucvMg14RKRRNHlIsm37beAeTMe6DcBIYIJt23vrHpIKtG/qOkTatKpieP1K2Poh+AXCVS/BOXc7XZWIiPwY8WeY9aRJZ0LFQTP1bsdCp6sSaRUsu5W1kKxrA15cXFxMZGSk0+WIOK80B16fArmbITACpr4BnUc6XZWIiDSW6lJ450bY9TlYfjDx7zDwBqerEvEJJSUlREVFAUTV9S+ol+bqbiciTijYZVp8526GsASY/pECkohIaxMUAVPfhjOvBdsDc34CS/+ivZREfgSFJJHWKms9vDAWijIhprOZu96+v9NViYhIU/APhEn/gRH3mvPFj8BHvzQNe0SkwRSSRFqjnYvM3PSKgyYY3boAYjs7XZWIiDQly4IxD8KEJwAL1r4A790GbvW9EmkohSSR1mbTu/DG1VBbDl1Gwc0fQXiC01WJiEhzGTIDprwIrgD45n148xptOivSQApJIq3J6n/B+7eB1w19r4Tr3jVz1UVEpG3pOxmuexsCQk1Dh1cvh4pCp6sSaTEUkkRaA9uGzx6GT39rzofeCZOfN3PURUSkbeo2Gm6cC8HRsP9LeGkClBxwuiqRFkEhSaSl83rho3thxVPmfPQDcPFj4NJfbxGRNi/lbLjlE4hoD/lb4YVxpvOpiHwvfYoSack8tTD7dlj7ImDBpU/Deb80i3dFREQAEnrBLZ9CbFcozoQXx0H2RqerEvFpCkkiLVVtFbw9DTa/Cy5/uPJ5GDzd6apERMQXxaSZEaWkM6E833RA3bPC6apEfJZCkkhLVF0KM6fAtx+DfzBc+wb0m+J0VSIi4svCE+DmeZA2AqpL4LXJsG2+01WJ+CSFJJGWpqIQXpkIe5ZDYATc8D50H+d0VSIi0hIER8EN70GPCeCphrdvgI1vO12ViM9RSBJpSUqy4aXxcGA9hMTCzR9Cp+FOVyUiIi1JQDBc/Rr0vw5sD8y+A9a+5HRVIj5FIUmkpSjMMItt87eZLkXTP4bkgU5XJSIiLZGfP1z+DJw9A7Bh3j2w+hmnqxLxGQpJIi1B3lZ48WIo2gsxnc3i24SeTlclIiItmcsFE/4Cw+8x55/eB0sfN3vvibRxCkkivi5rnZliV5YDCb1NQIrp5HRVIiLSGlgWjHkILvydOV/8R1j4gIKStHkKSSK+bO9qeOVyqDwEHQbDzR9BRJLTVYmISGtiWTDy1zDuT+Z81d/ho1+azcpF2iiFJBFftXspvD4Zakqh03lw4xwIjXW6KhERaa3OuRsu+ztgwdoXYM7d4HE7XZWIIxSSRHzRjs/gjauhtgK6jYHr34WgcKerEhGR1m7QTWZzcssPNr4J790C7hqnqxJpdgpJIr5m20fw1lRwV5l9LK59AwJCnK5KRETain5T4JrXwC8QtsyBt6+H2kqnqxJpVgpJIr7km9nwzo3gqYHeV8DVr4J/kNNViYhIW9PzEpj6FviHwI4FMPMqqC5zuiqRZqOQJOIrNr4Ns24BrxvOvAaufAH8ApyuSkRE2qpuo2Ha+xAYAXuWw+tXQlWJ01WJNAvLbmUtHi3LigSKi4uLiYyMdLockfpZ9wp8+D+ADQOnwWV/A5ef01WJNItaj5fiylqKK2upqPZQUeOmotZDZY2HihoPlbUeKmvcR27XuL24PTZur43b48Xjtan12ni8Xmo9Nh6v+XfNAizLwmWBy7JwucDCwqo7D/BzERTgIsjfRXCAH0H+LoL8634GmNvhQX6EBwUQEexPeLA/EUH+RAQHEBzgwrIsZ//HiTSXrHXw2iSoKoaOZ8MN70FwlNNVidRLSUkJUVFRAFG2bdc75SskiThtzX9h/q/M7bNvg/F/MRv8ibRAXq9NYUUNB8uqOVhaQ35ZFQdLzXlhec2RMFRcWUtJ3c/yGo/TZTeYv8siPNif8CB/YkIDiQ0LJC4skJiw42/H1Z0nRAYTHuTvdNkipy97I7xatyVF8kCYNhtCYpyuSuQHKSTVUUiSFmXVP2BB3QZ+5/wUxj5i9qsQ8UHVbg+5xdVkFVWSXVzJgaJKsoqqyC6uJLek+kgQOjyS01ARQf6EBfkTGuhHSKBf3U9/QgPMeUigH6EBfgT6u/D3c+HvsvD3s/B3Wfi5XAT4Wfi5zLmFhde2sQGvbeO1wbZtvF5zzeO1qfXYVLs9VLu9VNd6j952e6mu9VDl9lJR7aa0yk1ZtZuSqlrKqt2nvcdmeJA/iZFBJEUFkxgRTGJUMEmRwSRGBtM+KpgOMSHEhQVqhEp8V85mE5QqCiDpTG1NIS2CQlIdhSRpMZb+BRY/Ym6f9yuz27k+HImDvF6bvNJq9hSUk1lQwZ6CcvYWVLC/yASi/NLqer9WbFgg8eGBxIcH0S4iiPjwIGLDAokMCSDqmCO67mdEsD/+fr4/gmrbNuU1Hsqq3JRV11Jc6aaoooaC8hoOlddQWH70dkHdeWF5DWXV9dtrJiTAj5TYEFJiQkmJDaVjTAipseZ2SmyoRqPEeblb4NWJUJ4PiX1NUAqLd7oqkVNSSKqjkCQ+z7Zh8aOw7HFzfsHv4PxfO1uTtCmHymvYmV/GjtwyMg6Wsaeggr0F5WQWVlBV6/3e5wb5u0iODiE5Opj2USHmdpQZFWlXF4hiwwIJaAGBpzmVV7vJKakit7iKnJKq79yuJqe4krzS6h8cpWoXEUSX+DC6tAuna7swurQLo0t8OB1jQlpEyJRWIn87vHIZlOVCu15w01wIT3C6KpGTUkiqo5AkPs224fNHYPkT5vyiP8Dwnztbk7RKtm2TX1bNztyyI4FoR14pO/PKOFh26o0h/VwWHWNCSIsLIy02lLQ4M4LRITqE9lHBxGo6WJOpdnvIOlTJvkOV7CusYN+hCvYXVrLvUAX7Cis4VFF7yucG+rlIiwulS7sweiRG0CMpkh5JEXSKC1V4kqZxcIcJSqXZEN8dbvoQIpKcrkrkBApJdRSSxGd9NyCN+xOcc7ezNUmrUOvxsju/nC3ZxWw5UMKW7BK2HCj53g/VHaJDOCMxnC7x4XSKDyUtLoxOcaEkR4doFMhHlVTVkpFfzu6DZezOL2d3fjm78svIOFhOtfvkI4CB/i66J4bTIzGSnkkR9EiKoGf7CBIigpu5emmVCnaZoFSSBXHdTFCKTHa6KpHjKCTVUUgSn2Tb8PkfYPmT5lwBSU5TebX7SAg6HIi255ZSc5IPyS4LUmND6ZYQwRmJ4ZyREM4ZCRF0aRdGmNa2tBper01WUSW7D5azK6+M7TmlbMst5ducUiprT945MCEiiH4doujXMcr87BBFQqSCk5yGwgwTlIr3QUxnE5SiU5yuSuQIhaQ6Cknic2wbFv0eVjxlzi9+DIbd5WxN0iK4PV525JWxcV8RG+qOb3NLOVnzuPAgf3q1j6B3+0h6J0fSu30UZySGExyg/bbaKq/XJrOwgm05pWzPKWV7bgnbskvZU1B+0j9DiZF1walDNP06RnJmx2jiw4Oav3BpeYoy4eVLoWgvRKfCTfMgJs3pqkQAhaQjFJLEp5wQkP4Mw+50tibxWQeKKo+EoQ37ivg6q5iKk+whlBgZRN/kqLowZEJRSkwoLpfWCskPq6hxszW7hE37i9mcVczm/cXsyi87aXBKjQ1lUFoMZ6VGc1ZaDD0SI7TGSU6ueL8ZUSrcDVEpZkQptrPTVYkoJB2mkCQ+w7Zh0cOw4q/mXAFJjuH12uzML2NNRiFr9xTy5Z5DZBVVnvC48CB/zuwYRf+UaAakRNO/YzRJUZoWJY3r8DTOzfuL+TqrmE1ZJjh99yNCWKAf/VOi64JTDANTo4kODXSmaPE9JQdMUCrYaYLSzR9pREkcp5BURyFJfIJtw2cPwcqnzfn4x2HoHY6WJM6qcXvZnFXMl3tMKFq79xBF32ms4Oey6NU+4kgYGpASTdd24RohEkcUV9ayYV8R6/ceYn3mITZkFlF6kv2eeiRGMKxLLMO6xDGkcyxxmqLXtpXmwMuX1AWlVJj+kZmCJ+IQhaQ6CkniuBMC0l9g6O2OliTNz+3xsimrmFU7D7JqVwHr9h46oQNZSIAfZ6VFMzgtliGdYxmQEq2GCuKzPF6bHXmlrN9bxLq9h/gq8xC7D5af8LgeiREMrQtNQxWa2qaSbBOUCndBdJoZUVIzB3GIQlIdhSRxlG3DZw/Cyr+ZcwWkNsPrtdmeW8rKnQdZvauA9IxCyr7zrXtcWCCDO8VwdqdYzu4US+/kSLXblhatoKyaNRmFfLG7gC92F7I9t/SEx3RPDGdYlzhGdIvnnK5xRAQHOFCpNLuSA/DSBDiUATGd4Ob5ENXB6aqkDVJIqqOQJI6xbVj4AKz6uzmf8AQMmeFsTdKk9h+qYNm3B1m56yBf7CqgoPz4TVqjQgI4p0scw7vFcU7XOLq2C9dGrNKqFZbXsCbDBKYvdhewLef40OTnshiYEs15Z7TjvO7xnNkhSo0gWrPi/WZE6dAe0x58+nztoyTNTiGpjkKSOEIBqU2oqvXw5Z5ClmzPZ+m3+ezMKzvu/pAAP4Z0juXcrnEM7xZP7/aRWk8kbdrh0LRyZwErdh4k4zvT8yKC/RneNZ4RZ8Qz8ox2pMaFOlSpNJmifSYoFe2F2K5m6l1ke6erkjZEIamOQpI0u++uQVJAalX2FpSz9Nt8lmzPZ/WuguM253RZcFZqDCPOiOfcrvEMSIkm0F/fioucyr7CCpbvOMiKnfms2HGQkqrjp6R2igvlwp6JjO6VwNmdYvX3qbUoyqwLSpkQdwbcPA8ikpyuStoIhaQ6CknS7BY/Ckv/bG4rILV4tR4vX2YUsnBrLku255/wzXdiZBDnd2/H+d0TGNEtnqhQra8QOR0er82m/UUs33GQ5Tvy+SqzCPcxmzWFB/lz3hnxXNgzgVE9EmgXoQYQLdqhvSYoFe+D+O5mw9mIRKerkjZAIamOQpI0q2V/gc8fMbcvfgyG3eVsPXJaSqpqWbo9n8+25rJ4W95x3277uywGd4rh/O4JjOrRjp5JEVpXJNIESqtqWbHjIJ9vy2Px9jwOlh1d42dZcGbHaEb3TODCngn0SY7U38OWqDADXr4USvZDu54mKIW3c7oqaeUUkuooJEmzWfk3sw4J4KLfw/D/cbYeaZCsoko+25LLZ1tz+WJ3AbWeo78L48ICubBnAqN7JTK8m7pxiTQ3r9dmU1Yxn2/L4/NtuXyddfznmg7RIVzUO5GL+yZxdqdY/LT2r+Uo3F0XlLKgXS8z9S4s3umqpBVTSKqjkCTN4ot/wyf/a25f+DsY+Wtn65EfZNs23+aWMX9zNgu35LIl+/jfk13ahXFR70Qu6pXIwNQYfegS8SG5JVUs3pbHom15rNhx8Li1gbFhgVzUK5FxfRM5t2s8wQF+DlYq9VKwy0y9K82GhD5w04cQFud0VdJKKSTVUUiSJvfl8/DRL83tkb+BC+93th45Jdu22ZpdysdfZ/PR5mx25x9dX2RZMDgthjG9EhnTO5Gu7cIdrFRE6quq1sPyHQf55OscFm3Lpaii9sh9YYF+XNAzgXF9krigZwLh2pzZdxXsMvsoleVAYj+4aS6ExjpdlbRCCkl1FJKkSa1/Feb+zNwefg+Mech82hafYds23xwoYf7mbD7+Oue4xguBfi5Gdo9nbJ8kRvdMIC5cC8FFWrJaj5c1GYV8+k0On36TQ25J9ZH7Dv99v/TMZMb0TlRg8kUHd5gRpbJcSD4LbvwAgqOcrkpaGYWkOgpJ0mQ2vAkf3AXYMOwnMO6PCkg+wrZtNmcV89HmbD7enENmYcWR+wL9XYzq3o4J/dozuleC1heJtFJer83G/UV88k0OC77JPe4LkiB/Fxf2TOCy/slc0COBkEBNyfMZeVtNUKoogJRhcMN7EKSRfWk8Ckl1FJKkSWyeBe/PANsLZ8+ACX9RQPIBO/PKmLshizkbD7C34GgwCg5wcUGPBMb3a8+FmnIj0uYcXoM4b9MB5m3KPi4whQb6MaZXIpf1T2Zk93iC/BWYHJe9CV65FKqKodN5cP27EBDidFXSSigk1VFIkka3ZQ68Ox1sD5x1E1z6NLi0waFTcoqr+HDjAT7YkMU3B47+rgsJ8OPCnglM6NeeUT3aEaZgJCIcnYL74aYDzNuYTVZR5ZH7IoL9Gds7iYkDkhneNQ5/P/1ud8z+dfDq5VBTCt3GwLVvgL+mRMuPp5BURyFJGtW2+fDONPC6YcD1MPGfCkgOKK6oZf7X2czZkEV6RiGHf235uyxGdm/H5QOSGdMrUcFIRL6Xbdts2FfEhxuz+WjzgePWMLWLCGJi/2QmDeygfZicsnc1vD4ZaiugxyVw9SvgpynS8uMoJNVRSJJGs2MhvDkVvLXQ7yqY9Cy4NC2juVS7PSzamsfsr7JYsj3vuH2MhnSKZeKAZCb0a09sWKCDVYpIS+X12qzde4gPNx5g3qYDHDqmS173xHAmDezIFQOTaR+laV/NavcSmHk1eKqhz2S48nn92ys/ikJSHYUkaRTH/pLufTlc+SL4aZSiqdm2zab9xby3fj9zNhyguPLoh5aeSRFcPqADEwck0yFaH1pEpPHUuL0s/Taf2V/t57OtedS4vYBZenpOlzgmn9WRi/smaX1jc/l2Abx1nfmSsv9UuPxfmsUhp00hqY5CkvxomV/Aa5M03N+M8kqqmP1VFrPW7WdHXtmR6+2jgrliYAeuGNCBHkkRDlYoIm1FcWUt8zdnM3t9Fmv2FB65HhzgYmzvJK4c1JER3eK14XRT2/ohvHOTWQ88aDpc+lc1TJLTopBURyFJfpQDG+CVy6C6BLqOhqlvauFoE6mq9fDZ1lzeW7efpd/m4637VRTk7+LivklMGdSRc7vqg4iIOGdfYQUffJXF7K+y2H1Mh7zkqGCmDOrIVYNTSIkNdbDCVm7zLHjvNsCGoXfBxX9SUJIGU0iqo5Akpy1vG7w0HioLIfVcs1dDoP7xa2yb9xfz9tpM5m44QEmV+8j1QWkxTBnUkUvObE+k9jISER9yuOHD7K+yTpgKPLxbHFcPTmFcnySCA7R2ptF9NRPm3G1uaxN3OQ0KSXUUkuS0FO6GF8dDWU7drt9zIFh/fhpLSVUtczYc4K01mce17W4fFczkszpw5Vkd6dJOmweKiO+rqvXw6Tc5vLN2Hyt3Fhy5HhUSwBUDkrlqcAp9O0Q5WGEr9OXz8NEvze1Rv4VR/+tsPdKiKCTVUUiSBivebwJScSYk9IabP4LQWKeravFs2+arfUW8mZ7JvE3ZVNZ6AAj0M9Pprh6cwjld4zSdTkRarH2FFby7bj+z1u7jQHHVket9kiO55uwULh/QgagQjYw3itXPwKf3mdtjHoYR9zhbj7QYCkl1FJKkQcryzBS7gp0Q2xWmfwwRiU5X1aIVV9Ty/lf7eWvNPrbnlh653i0hnGvPTmHyWR3VtltEWhWP12bFzoO8s3YfC7/JpcZjuuMFB7i47Mxkrh+WRv+OUdp76cda9gR8/gdze8ITMGSGs/VIi6CQVEchSeqtotA0acj9GqJSTECKTnG6qhbJtm2+3HOIN9dkMn9zNtV17XOD/F1ccmZ7rhuSyqC0GH1AEJFWr7C8hg++yuLtL4//oqhPciQ3DEtjYv9kbXz9Yyz6PSx/0tye9Bz0v8bZesTnKSTVUUiSeqkuhVcvh6x1EJ5oAlJcV6eranHKqt3MXr+f177Yy7e5R1t390yK4LqhqZpqIiJtlm3brM88xMwvMpm3OfvI3kvhQf5MGtiB64el0jNJn1MazLbh49/AmufA8oOrX4VelzpdlfgwhaQ6Cknyg2oqYOZVsHcFhMTC9PmQ0MvpqlqUHbmlvPbFXt5fn0VZtelQFxLgx8T+yUwdmqppJSIixygsr+G9dfuZmb6XPQUVR64PTovh+mGpjO/bXp3xGsLrNR3vNr4JfoFw3TvQ9QKnqxIfpZBURyFJvpe7xuzivXMhBEXCTXMheaDTVbUItR4vC7fk8urqPXyx++gGi13ahTFtWBpXDuqo1t0iIt/D67VZvbuAmel7WfBNLu66DeKiQwO4ZnAKNwxL075L9eVxw6ybzaazAaGmK23KEKerEh+kkFRHIUlOyeOGWdNh61zzC/WG9yHtHKer8nl5JVW8sSaTN9dkkltSDYDLgjG9ErnxnE4M7xanUSMRkQbKK6ni7S/38eaazCOd8Q7/br15eCfO6aLfrT/IXQ1vXgu7PofgKNOdNqmf01WJj/HpkGRZ1t3Ar4H2wDfAPbZtLz/FY2cANwJ96y6tA+6zbXtNPd9LIUlO5PXCB3fBprc0NF8PhxsxvLJ6D59+nXPk28748ECuPTuV64amkhwd4myRIiKtgMdr8/m2PF5ZtYcVOw8eud4jMYKbzu3EFQOTCQ1Uo4dTqimH1ybDvi8grJ1ZYxx/htNViQ/x2ZBkWdY1wGvA3cBK4A7gNqC3bduZJ3n8zLrHrQKqgN8Ak4E+tm1n1eP9FJLkeLZtNqFb+4JZ5HnNa9DzEqer8knVbg/zNmbz4sqM4zZ9HZQWw43npHFx3ySC/DVvXkSkKezILeWV1Xt4b13Wkb3lIoP9uXZIKtM0Fe/UKovglUshZzNEdoBbPoHoVKerEh/hyyEpHVhv2/Zdx1zbCnxg2/Zv6/F8P+AQ8FPbtl+tx+MVkuR4Cx+AlX8DLLjyeeg3xemKfE5BWTUz0zN57Yu95JeaKXVB/i4mDezAtHPS6JOs3eNFRJpLcWUt767dx6ur95JZaBo9WIen4p3biXO7aireCcoPmn0PD34LsV1g+ifa91AAHw1JlmUFAhXAVbZtzz7m+t+AAbZtn1+P14gA8upeY95J7g8Cgo65FAHsV0gSAFb8FT57yNy+7O8w6CZHy/E123JKeGnFHmZvyDrSnjYxMogbz+nE1CGp2vRVRMRBHq/Nku15vLxqD8t3HJ2K1z0xnFuGd+aKgR3UFe9YxVnw4sVQnAkJfeDmeRAa63RV4jBfDUnJQBYw3LbtVcdcvw+4ybbtHvV4jWeAcUBf27arTnL/Q8CD372ukCSsfQnm3WNuj/0jnPtTZ+vxEV6vzeLteby4MoOVOwuOXD+zYxS3jujM+L7tCfR3OVihiIh81868Ul5ZtZf31u+nosZMxYsPD2TasE7cMCyVuPCgH3iFNqJglxlRKsuFDoPhxg8gKMLpqsRBvh6SzrVte/Ux1+8Hptm23fMHnv8b4H+BUbZtbzrFYzSSJCf6+j2YdStgw3m/gtH/53RFjiuvdvPe+v28tHIPGQfLAdNJ6eK+SdwyvDOD0mI0fUNExMeVVNXy9pp9vLQy40hXvCB/F5PP6sitIzrTLSHc4Qp9QO4WeHkCVB6CziPhunchINjpqsQhvhqSTnu6nWVZvwJ+B4yxbXttA95Ta5Lauh2fmZag3loYfAtc8pSZzN1G5ZVW8fLKPbz+xV5KqszGrxHB/kwdksqN56TRMUYLgUVEWppaj5f5m7N5fnkGm7OKj1wf3TOBW8/rrBbiWevglYlQUwbdx5umTX7ay68t8smQBEcaN6yzbfvuY65tAeacqnGDZVm/xgSkcbZtf9HA91NIassyv4BXrwB3JfS9Eib/F1xtc772zrwynl++m/fXZ1HjMeuNOsWFMn14Z64c1JHwILWUFRFp6WzbZk1GIf9dnsGibbkc/ljXt0Mkt43owiVntifAr41Ood6zAl6/EtxV0HcKTH6uzX4maMt8OSQdbgF+J7AauB2YgWnpvdeyrFeBrMOBqW6K3R+A6zCtwA8rs227rB7vp5DUVuVshpcugepi6HYRXPsG+Le9xgNr9xTy7LLdLNySe+TaWanR3HF+Vy7qlYjL1Ya/WRQRacV255fx4soMZq3bT1Wt+XIsKTKYm4d34rqhqUQGt8GRlG8XwFtTwevW7JI2ymdDEhzZTPY3mM1kvwZ+Ydv2srr7lgB7bNu+ue58D5B2kpd52Lbth+rxXgpJbVHBLtPRpjwPUobBtNkQ2HamkXm9Ngu35vLcst2s23voyPWLeidyx8guDO6k7j4iIm1FYXkNb6Tv5eVVezlYZrZ1iAjy5/phadwyohMJEW1sfc6x65RH/gYuvN/piqQZ+XRIak4KSW1QyQF4cRwUZUJiP9PyMyTa6aqaRVWth9lfZfHf5bvZnW+aMQT6uZh8VgduO6+LFvCKiLRh1W4PczYc4L/LdrMjz0zGCfR3MWVQR24/rwud4sMcrrAZffkCfHSvuX3xYzDsru9/vLQaCkl1FJLamIpC0+ozf5vZPO6WTyE8wemqmlxxRS2vp/9/9u47PKoy////cya9h5AEQigpJKF3RSmCBaSIWAAb0u297Wd1P/v9fn7Xb9fP7tpQVrAhdkVWAUWkSBNB6b2kkkIgJBBSSEiZmfP9Y4YRlChgkpPyelwXF8OZOzNvlJzM65z7ft9ZzNuQ+fNVQl9P7r6iA1MGxBAZ3MyuEoqISI0cDoPVB/OZvTaN7dlFgLO76cjuUTwwJJ5u0c1kw/DvX4DVf3M+vvlN6Hm7ufVIvVBIclFIakYqS+GDsc4ONkFRzoDU4nwzNZuO/NIK5q4/xEc/ZVHm2iejTYgv0wbFcvvl7dWMQUREamQYBlsyTzJnbRprkgvcxwcnhPPA0Pim3xHPMGD5c/DTbLB4wO0fQ9JIs6uSOqaQ5KKQ1EzYKuHj8XBoHfi1gKnLIPI3t91q1A6fLOfNdRnM35pDlc25GLdT6yDuGxLHDT3aNN/ORSIickkOHC3hzXXpfL37KHaH87Ngz7YhPDA0nuFdWjfdJj8OByx6AHZ/Bp6+zjXMHQaYXZXUIYUkF4WkZsBug/9MgQNfg3cgTPoK2vY1u6o6kV5witlr0lm8Mxeb64dY7/ahPHx1R6ZYMlsAACAASURBVK7pFNm0r/iJiEidyyks5+31GczfkkOl6yJcXEQA918Vz029o/H2bIIX4ezVMH8ipCwDn2CY8g1E9TC7KqkjCkkuCklNnGHA4odh50fg4Q13LYC4oWZXVev25hYzZ206S/cede95MahjOA9e3QymQ4iISL07fqqS9zdm8v7GTPfG49Ghftw/JI7x/drh69XE9heqPg0f3gLZGyEgEqYtg5bxZlcldUAhyUUhqQkzDFjx3/Djv8FihQkfQOcxZldVq7ZmFvL6mnPnil/XuRUPXR1P7/YtTKxMRESag1OVNj7dlM1b6zMoKHU2BooM8uHeq+K4q38H/LybUFiqKHbur3hsD4S2h2krIDjK7KqklikkuSgkNWHfvwir/3/n47GvQ++J5tZTSwzDYH3qcV5fk8amQ4WAs+vQDT3a8ODV8XRqrX/HIiJSvyqq7Xy+NYc31qZzpLgCgJYB3kwfHMukK2OaTqOgU/nObUQKMyCyC0xd6lzrLE2GQpKLQlITdfb+Btc/D1c+ZG49tcAwDL47kM+s1ansPlwMgJeHhVv7tOX+IfHNa/8KERFpkKpsDr7cfpjZa9PJLiwHIMTPi2kDY5kyIIYQfy+TK6wFJzNh7vVwKg/a9XdtSK+fwU2FQpKLQlITtG8RLJgCGDD4abj2r2ZX9IcYhsHK/cd4dVUq+444v1d9vazccXl77hkcR5tQP5MrFBEROZfN7mDxziO8vjbNvXl5kI8nkwZ0YPqgOMICvE2u8A86th/mjXBOwet4Hdz+KXg28r+TAApJbgpJTUzGOvh4HNiroO8UuGEmNNKmBYZhsGL/MV79LpX9R53fo/7eHky6MoYZg2MJD/QxuUIREZHfZncYLN1zlH+vTiP5WCkAfl4eTLyiPfdcFUdkUCPezDxns3P/xepy6DYObnkbrE2wu18zo5DkopDUhBzd5VxQWVXqbNAw/n2wNr4Fow6HKxytSuWAKxwFeHsweUAMMwY3gatvIiLS7DgcBisPHGPW6lT25jp/tnl7Wrnz8vY8ODSeyOBGGpZSv4NPbwOHDS67B0a90GgvzoqTQpKLQlITcSLduZCyrABiBsNd/wGvxnXCdTgMlu/L49VVqRzMc15tC/D2YMrAGGYMiqOFwpGIiDRyhmGwNqWAWatS2Z5dBICPp5W7+nfg/qGN9M7Snv/AFzMAA4b8Ga5+1uyK5A9QSHJRSGoCSvNg7nAoyoJW3WHqN+AbYnZVF8zhMFi2L4/XzgpHgT6eTBkQw/RBsQpHIiLS5BiGwYa0E7zyXQrbsk4CzvW2d1/RgfuGxDe+KeVb3oFvnnI+Hvkv6H+fufXIJVNIclFIauTO3rOgRYxzz4KgVmZXdUEcDoNv9zrD0Zl52kE+nkwdGMO0QbGE+isciYhI02YYBt+nHueVlSnszHHeWfLz8mDSlR2496o4WjamsLTuX7Dm787Ht86F7uPMrUcuiUKSi0JSI1ZdAR/dClk/OHe/nr4cwuLMrup3nblzNPO7FFKOnQIgyNeTqQNjmT4wtmm0RxUREbkIZ6bhzVyZwi7XNhdnmhXde1UjWY9rGPDtf8HmN8HqBXd9DvHXmF2VXCSFJBeFpEbKYYfPJ8HBJeAd5JxiF9XT7Kp+k2EYrDqQz8srU9zd6oJ8PZk+KJapA2MJ8VM4EhGR5s0wDNYk5/PKylT25DrD0pn1ufcMjmv4sywcDvhiOuz7ErwDYfLXEN3H7KrkIigkuSgkNUKGAV8/BtvfBw9vmPgFxF5ldlU1MgyDH9KO8+KKFHa5phIE+jjD0bRBCkciIiK/dGYD9Znfpbj3CAx0TUmfMSiuYc+6sFXCJxMgYy34h8P0FdAy3uyq5AIpJLkoJDVCq/8G378AWGDC+9BlrNkV1WhTxgleWpnC5kOFgHOe9ZSBMdw7WN3qREREfs+ZPQNnfvfzthhBPp5MHxzL9EGxBPk20LBUWQrv3QBHd0JoB2dQCmptdlVyARSSXBSSGplNb8K3f3I+vuEV6DfN3HpqsCP7JC+vTGF96nHAuRfExP4deGBoPBFBjWgRqoiISANwZpuMmd/93Oyohb8X9w+JZ9KVMfh5N8B9EU8VwLvDoTCjUXbfba4UklwUkhqRvV/Af6YDBgx9Dob+l9kV/cq+I8W8sjKF7w7kA+BptXD75e146OqORIX4mVydiIhI4+ZwGCzde5SXV6aQUVAGQGSQD49c05HbLmuPt6fV5Ap/ofCQc5uSsvxGu49jc6OQ5KKQ1Eikr4aPJ4CjukHuaJ16rJRXvkth6Z48AKwWuLVPWx69NoF2Yf4mVyciItK02OwOFu7IZeZ3qeQWnQagbQs/Hr8ukZt7R+NhbTifETi6G+aNgqpS6HwjjH8PrA3wzpcACkluCkmNQO5257ze6jLoerNz74EGcnLJPF7Gq6tSWbQzF8Nw5rYxPdrw2HUJxEcEml2eiIhIk1ZpszN/Sw6zVqdRUFoJQHxEAE8OS2Jkt9ZYG0pYOvS9c9sSe5VzqcDolxvUxV75mUKSi0JSA3c8zTmft/wExA6BuxaAp/lreo4Wn+bV71JZsO0wdofze2JE19Y8MSyRpNZBJlcnIiLSvJyusvP+j5m8sS6dovJqALq2Cebp4UkMTYrA0hACyb5FsGAKzmUDz8LQP5tdkZyHQpKLQlIDVnLUOY+3OBuiesGUJeBjbgA5WVbF7LVpvP9jFlU2BwBXJ0Xw5LAkurfVYkwREREzlVRUM3f9Id5Zn0FZlR2Afh1a8PT1SVwR19Lk6oAtc+GbJ52PR78Ml003tx75FYUkF4WkBup0kXP+bv4+CIuHacshMMK0csoqbbz7wyHe+j6D0kobAJfHhPGnEUn0iwkzrS4RERH5tcKyKt5Yl877GzOpdF3UHJwQztPDk+jZLtTc4tb8L6z7B41hK5PmSCHJRSGpAao+DR/eDNk/QmAr594CLWJMKaXK5uDTzdnMWp3K8VNVAHSOCuZPI5IYmthAbt+LiIjIeR0rqWDW6lQ+25yDzTU9fniXVjxzfRIJrUyanWIYsOQJ2DYPPLxh4pcQO9icWuRXFJJcFJIaGLsNPr8bkpeCTwhMXQqtu9V/GQ6Dr3bl8vLKFHIKnV1z2of589TwRMb0aNNwFoKKiIjI78opLGfmd6ks3HEYh/FzF9onhiXSJtSELTocdlgwGQ58DT7Brs873eu/DvkVhSQXhaQGxDDg60dh+wfg4QN3L4SYgfVcgsHqg/m8sDyZg3nOzeoignx49NoEbuvXruHtvyAiIiIXLC2/lBeWJ7N83zHAudn7lAExPDg0nlB/7/otproCProFsjaYPnNGfqaQ5KKQ1ICseR7W/RMsVpjwIXS+oV7ffktmIf/89iBbs04CEOTryf1D4pk6MAZ/b896rUVERETqzrask/xz2UE2HyoEfv6ZP21gLH7e9bjNyOkieG80HNsLYXEwbYWpa7BFIclNIamB2Pquc34uwA0zod/Uenvr/UdKeHFFMqsP5gPg42ll6sBY7h8SV/9XlURERKReGIbB2uQC/rnsoHv2SGSQD49fl8iEfm3x9Kin2SMlR53bnRRlQ5veMPlr07v5NmcKSS4KSQ3AgSXOdUiGA4b8F1z9XL28bdaJMl5emcJXu45gGOBhtXDbZe149JoEWof41ksNIiIiYi6Hw2DxrlxeWpHC4ZPOdchx4QE8fb1zQ9p6adJ09r6QcVfDnZ+Dpy7UmkEhyUUhyWTZP8EHY8FWAX0mwZjX6nwH6oLSSl5blcqnm7PdnW5u6BHFU8OTiA0PqNP3FhERkYap0mbnk03ZzFqdRmGZs6Ntz7Yh/NeITgzoGF73BeRug/fGQHUZdBsHt7wNVq2Frm8KSS4KSSYqSHZuFltRBIkj4LaPwaPu1v6UVdp4e30Gb3//8wZzVyVG8Kfrk+gWrY1gRUREBEorqnnbtSFtuevzwuCEcP5rRKe6/7yQtgo+mQAOG1zxIIz437p9P/kVhSQXhSSTlByFucOgOAfaXgaTvgJv/zp5K5vdwfytObyyMpXjpyoB15WhkZ0YEF8PV4ZERESk0SkoreTfq1P5ZHM21Xbn598be7bhqeGJdGhZhzNPdi+AL2c4Hw//Gwx4pO7eS35FIclFIckEFcUwb5Szk0vLjs5OLgEta/1tDMNgxf5j/HPZQTIKygDnXkd/GpHE6O5R2ghWREREflf2iXJeWpnM4p1HAPC0Wrizf3sevTaB8ECfunnTjbNgxX87H9/yDvQYXzfvI7+ikOSikFTPbJXw0a2Qud61J8BKaNGh1t9mW9ZJ/nfpAXc777AAbx69piN39u+gvY5ERETkou3NLeZfy5P5PqUAgABvD+4fEs/0wbF1s1XIsufgp9fB6gUT/wNxQ2v/PeRXFJJcFJLqkcMBX0yDfQvBO8i5u3RUj1p9i4yCU/xrWTLL9uUB4OtlZfqgWO4bEk+wr1etvpeIiIg0PxvTjvOPZQfZfbgYgFbBPjw5LJFxfdvhYa3FWSoOh3Pa3d4v6uxzk/yaQpKLQlI9MQxY9ixsmlMnV0QKSit5dVUKn27Owe4wsFpgfN92PDEsUe28RUREpFY5HAZL9hzlX8sOutuGJ7YK5NmRnRmaFFF7U/p/NQNnBbSIqZ3XlvNSSHJRSKonG16Flf/H+fjWudB9XK287Pk61l3bKZL/GtmJxFbaiE1ERETqTqXNzoc/ZjFrdRrFp6sBGBDfkmdHdqZ721rqhFdPa7nFSSHJRSGpHuyaDwvvdT6upS4tNXWse3ZUZ66I04lDRERE6k9xeTWz16Yxb2MmVTYHAGN7teHp4Um0C6uF7r0lR53bphRn13lX4OZOIclFIamOpa+Gj8e7+v0/BCOe/0Mvd76OdR1a+vPM9epYJyIiIuY6fLKcF5cns8jVCc/bw8qUgTE8NLQjIf5/cG10QQq8OxxOn6yX/SWbK4UkF4WkOnRkJ7w3GqpOQbdbnS0s/8DO0epYJyIiIo3B3txinl96gI3pJwAI8fPi4as7MmlAB3w8PS79hbM3wQc3gq0C+kyCMa+BLhDXKoUkF4WkOlJ4yHlbuCwfYq+Cu/4Dnpe2l8D5OtbNGBTHfUPiCFLHOhEREWmADMNgbUoB/1h6kORjpQC0beHHM9cnMaZHG6yX2gnv4FKYfxcYDhjyZ7j62VqsWhSSXBSS6kDZcWdAKkyHVt2dLSt9L/6/bWFZFa+tSuWjn7KwuTrWTejXjsevU8c6ERERaRzsDoMvth3mpZXJHCtxrqPuHh3Cs6M6MSA+/NJedOs8WPK48/ENM6Hf1FqqVhSSXBSSallVGbw/BnK3QUh7mLESglpf1EtU2uy8vzGTWavTKK2wAXBNp0j+rI51IiIi0kiVV9l494dDvLEug1OVtfD5Zs3zsO6fYLE61yd1GlXLFTdPCkkuCkm1yF4Nn90JqSvArwVMXwnhCRf85YZhsGT3Uf551p4DXaKC+cvozgzseIlXWkREREQakOOnKnltVSqfbMo+Z6bME8MSaRV8ETNlDAO+fhS2fwCefjD5K2h3ed0V3kwoJLkoJNUSw4CvHoYdH13SN+q2rEL+9s0BdmQXAc7dq58ensQtfdrW7u7VIiIiIg3AL9dc+3l5cN+QOO69Kg5/7wvsWme3OdcnpSxzXqCetgIiEuuw6qZPIclFIamWrP4bfP/CRd/yzT5Rzj+XHeSbPUcB8Pf24P4h8cwYHHvhJwgRERGRRmprZiHPLz3A9rMuFD81PIlbL/RCcVUZvH8j5G51LnWYvgKCo+q46qZLIclFIakWbJkL3zzpfDzmVeg75Xe/pLi8mn+vSeX9jVlU2R3uW81PDksk8mJuNYuIiIg0coZhsHRPHv9YdoCcQueSg85RwfxlVGcGJVzAkoOyEzB32FlNs74B35A6rrppUkhyUUj6gw4sgc/vdrahHPosDP3zbw6vsjn46KcsXludSlF5NQCDE8J5blRnOkfpv7+IiIg0XzU1r3puVCc6Rv5Oc4eTmfDOsFrZfqU5U0hyUUj6A7J/gg/GujY0m+y8i1TDhmaGYbB83zH+8e0BMk+UA5DYKpDnRnVmaFJkfVYtIiIi0qD9chsUD6uFOy53boMSHvgbwefoLpg3CqpOQbdb4ZZ3wGqtv8KbAIUkF4WkS5R/EN69HiqKIGkUTPgQPM6/hmhXThF//+YAmzMLAQgP9OGp4YmM79sWTw9944qIiIicT0bBKf7x7UFW7D8GQKCPJw8MjWf6oFh8vTzO/0Xpq+Hj8eCwwZUPw/V/r8eKGz+FJBeFpEtQcsR5O7fkMLS9HCYtBm//Xw07fLKcF5Yns3jnEQB8vazcMziO+4bEE+ijpgwiIiIiF+KnjBP87Zv97M11fmaPDvXjTyOSGNOjDdbzNXfY/Tl8eY/z8fC/w4CH67Haxk0hyUUh6SKdLoJ5IyF/P7RMcHZQ8Q87Z0hpRTWz16Yz94dDVNkcWCxwc+9onrk+iagQP5MKFxEREWm8HA6Dxbty+deyZI4WVwDQs20I/31DFy6LCfv1F2x4FVb+H+fjW+dC93H1WG3jpZDkopB0Eaor4KNbIesHCGzl3Cy2RQf30za7g0+35DBzZQonyqoAuDKuJX8Z3Zlu0eqwIiIiIvJHVVTbmfvDIWavSaOsyg7AiK6t+fPITsSEB/w80DBg2bOwaQ5YvWDifyBuqCk1NyYKSS4KSRfI4YD/TIX9i8A7CKYuhagegLMpw+qD+Ty/9ADpBWUAxEUE8NzIzlzbORJLDc0cREREROTSFJRW8vLKFOZvycZhgJeHhbuviOHRazsS6u/tHORwwBfTYN/CX31+k/NTSHJRSLoAhgHL/gyb3nBdifgC4oYAsO9IMX//5gAb008AEBbgzRPXJXD75e3xUlMGERERkTqVcqyU55ceYG1yAQAhfl48ck1HJl0Zg7enFWyVzplAmevPOxNIzqWQ5KKQdAF+mAnf/V/nY9ec1rziCl5ckcwX2w9jGODtaWXawFgevDqeYF8vc+sVERERaWbWpxbw928OcDCvFIAOLf3584hOjOjWGktlCbw7EvL31bimXJwUklwUkn7Hrs9g4X3Ox9c/T1mf+3hzXTpvrc+gotoBwI092/DM9Um0C/t1hzsRERERqR92h8F/tuXw4ooUCkorAejXoQV/Gd2Z3qGnYe5wKM6BtpfBpK/O2524uVNIclFI+g1pq+CTCeCw4bjiYT4Pu4+XVv78TXdZTAv+MroLvdqFmlyoiIiIiJxRVmnjze8zeOv79HMuaj93uYXWC8Y697lMHAm3fVTjPpfNlUKSi0JSDY7sgHmjobqM/A43MrloOgeOOZsydGjpz7MjO3F919ZqyiAiIiLSQJ1vecRfe5QwMeVRLLYK6DMZxrwK+jzndqkhqV5W4lsslgctFsshi8VSYbFYtlkslsG/M/5Wi8Wy32KxVLp+v7k+6myyCjOcOzVXl7HPpzcDk8dx4FgZIX5e/PWGLqx8YggjukUpIImIiIg0YK1DfHlxfE++fngQA+JbUmVz8NftgTzleBQHVtj+Pnz/gtllNgl1HpIsFsttwEzg70BvYD3wrcViaV/D+CuB+cCHQE/X759bLJb+dV1rk3SqANsHt0BZAfscHbit+CHw8GL6oFjWPTOU6YNinZ1SRERERKRR6BYdwscz+jN3cj/iIwL4srwXf62e4nxyzd8xtr1van1NQZ1Pt7NYLJuA7YZhPHDWsQPAIsMwnj3P+PlAsGEYI886tgw4aRjGHRfwfg1qul1VVVWNz1mtVjw9PS9orMViwcvL66LGHj5+iEXzxzE1L5U8RwQTqv5Kv26deHp4Eh1aBpz3daurq6np38TFjAXw9va+pLE2mw2Hw1ErY728vNx3yOpqrN1ux26318pYT09PrFZrgxnrcDiw2Ww1jvXw8MDDw6PBjDUMg+rq6loZe/b3Z12NBXPPEWfU1ve9zhHnH6tzhM4ROkdc/FjQOeJCx1bbHXy+JZtXV6Ux1fYZj3ktZqePLzt63cdd1/53ja9bH+eIhuBSp9vV6coui8XiDfQF/vGLp1YAA2r4siuBV35xbDnweA3v4QP4nHUo6OIrrTvPP/98jc8lJCRw1113uf/8wgsv1HjijImJYcqUKe4/z5w5k/Ly8vOObdOmDffeey//XHA7awOrmJXqj0dpWwZ23E/UoUw+fnOZe2xERAQPPfSQ+89vvfUWBQUF533d0NBQHn/85/8N8+bN48iRI+cd6+/vz5/+9Cf3nz/++GMyMzPPO9bLy4u//OUv7j/Pnz+f1NTU844F+J//+R/34y+//JL9+/fXOPa5555znwyXLFnCzp07axz7zDPPEBDgDI/Lly9ny5YtNY59/PHHCQ11NrhYtWoVGzdurHHsgw8+SGRkJADr169n7dq1NY695557iI6OBuCnn35i5cqVNY6dMmUKMTExAGzbto2lS5fWOPbOO+8kMTERgD179rBo0aIax44fP56uXbsCcODAARYsWFDj2JtuuolevXoBkJaWxieffFLj2FGjRnH55ZcDkJ2dzXvvvVfj2GHDhjFw4EAAjh49yttvv13j2KFDhzJ06FAACgoKmD17do1jBwwYwPDhwwEoLi5m5syZNY697LLLGD16NADl5eW88ELN0xd69erFTTfdBDh/kP/W932XLl2YMGGC+89mniPOeP311ykqKjrvWJ0jfqZzhJPOEU46RzjpHPEzs88RI+120hPGcuepFPYElWFf/yE/LT5EVOv4846vj3NEY1bXMS8c8ACO/eL4MaB1DV/T+iLHPwsUn/Xr8CVV2gQltbueCJuDEquF414H+On4t+SV5ZldloiIiIjUoip7FTvyt7Cm+H/YE1SGxYCO1QGEhEWaXVqjVafT7SwWSxsgFxhgGMaPZx3/C3C3YRidzvM1VcBkwzA+PevYXcBcwzB8zzP+fHeSDmu6nReGYVBy6gQfJc9n3r55nLadBmBY+2E80vsR2gW3023yWhirqTSaSqOpNBc/FnSOuJSxOkf8sbE6R+gccbFjG/o5wuawsTBlIW/seYPCikIsVgv92/Tn6V6P0CGkE56/Me1N0+1+W12HJG+gHBhvGMbCs46/CvQyDGPIeb4mG3jFMIxXzjr2BPC4YRgdLuA9G9SapIaioLyA13e+zsK0hTgMB55WT+7sdCf39riXEJ8Qs8sTERERkQtkGAbrc9fz0taXyCjOACAmOIYn+z7J0HZD1bH4LA0yJIG7ccM2wzAePOvYfmDxbzRuCDIMY9RZx74Fihpj44aGJuVkCi9vfZkNRzYAEOITwv097ue2pNvw8vD6na8WERERETMlFybzwtYX2HR0EwAtfFrwQK8HGJc4Di+rPsv9UkMOSbfhbON9P/AjcC9wD9DVMIwsi8XyAZB7JjBZLJYBwPfAX4DFwFjgb8AgwzA2XcD7KSRdgA25G3hx64ukFaUB0D6oPU/2fZJr2l+jqw8iIiIiDUx+eT6zdsxicdpiDAy8rF5M7DKRe7rfQ5B3g+pb1qA02JAEzs1kgT8BUcBe4AnDML53PbcWyDQMY8pZ48fhDEZxQDrwF8MwvrzA91JIukA2h41FaYv4945/c6LiBAB9IvvwzGXP0C28m8nViYiIiEh5dTnv7XuP9/a9515fPiJmBI/1eYy2QW1Nrq7ha9AhqT4pJF28suoy5u2dx/v73qfCXgHAqNhRPNbnMdoEtjG5OhEREZHmx+6w81X6V8zaMYuC08626r0ievH0ZU/TM6KnydU1HgpJLgpJly6vLI9ZO2bxdfrXGBh4W725u8vdTO8+XbdxRUREROrJj0d+5MWtL5JyMgWAtoFteaLvEwzrMEzLIi6SQpKLQtIfd+DEAV7c+iKb8zYDEOYbxgM9nQsCPa11uv+wiIiISLOVXpTOS1tfYn3uegCCvIO4r8d93NHpDrw9vH/nq+V8FJJcFJJqh2EYfH/4e17a9hKHig8BEBsSy1N9n+KqtlfpKoaIiIhILTlx+gSzd87mi9QvsBt2PC2e3N7pdu7rcR+hvqFml9eoKSS5KCTVrmpHNV+kfMHsnbM5WXkSgP6t+/NUv6fo3LKzydWJiIiINF4Vtgo+OvAR7+x5h7LqMgCubX8tT/R9gg7Bv7s9qFwAhSQXhaS6UVpVyjt73uGj/R9R5ajCgoUx8WN4tPejtApoZXZ5IiIiIo2Gw3DwTcY3vLbjNfLK8gDo0rILz/R7hn6t+5lcXdOikOSikFS3ck/l8ur2V/n20LcA+Hr4MrnrZKZ1m4a/l7/J1YmIiIg0bNuObeOFLS+w78Q+AFoHtOaxPo8xKnYUVovV5OqaHoUkF4Wk+rGnYA8vbn2R7fnbAWjp25JHej/CTR1vwsPqYXJ1IiIiIg1LVkkWr2x7hVXZqwAI8ApgRvcZTOw8EV9PX5Ora7oUklwUkuqPYRisyl7FK9teIbs0G4COoR15ut/TDIweaHJ1IiIiIuYrqijijd1vMP/gfGyGDavFyriEcTzQ6wHC/cLNLq/JU0hyUUiqf9X2auYnz2fOrjmUVDn/7Q1sM5Cn+j1FQosEk6sTERERqX9V9io+Pfgpb+5+k9KqUgAGRQ/iqb5P0bFFR5Oraz4UklwUksxTXFnMW7vf4pODn2BzOK+U3NzxZh7u/bCulIiIiEizYBgGK7NW8sq2Vzh86jAAiS0SearfUwxoM8Dk6pofhSQXhSTz5ZTk8Mr2V1iZtRIAP08/pnWbxuSuk/Hz9DO5OhEREZG6sf3Ydl7a9hK7C3YDEOEXwSO9H+HG+Bu1ZtskCkkuCkkNx478Hby45UV2H3eeKCL9I3m096OMiR+j7i0iIiLSZBwqPsTMbTNZnbMacF4gntx1MlO7TlX3X5MpJLkoJDUshmGwPHM5M7fPJPdULgCdwjrxdL+n6R/V3+TqRERERC7d8dPHeWPXG/wn5T/YDTtWi5VbEm7hwZ4PEuEfYXZ5gkKSm0JSw1Rpk/ZXZQAAIABJREFUr+STA5/w9u63Ka12Ll4cHD2YJ/o+oeYOIiIi0qiUV5fzwf4PmLd3HuW2cgCGth3K430fJz403uTq5GwKSS4KSQ3byYqTzNk1hwXJC9xtMG+Mv5GHej1E64DWZpcnIiIiUiO7w86itEW8vvN1Ck4XANC1ZVee6vcUl7W+zOTq5HwUklwUkhqHrJIsXtv+GiuyVgDg4+HD3V3uZlq3aQR5B5lcnYiIiMjPDMNgfe56Xtn2CmlFaQBEB0bzWJ/HuD7meq21bsAUklwUkhqXXQW7eHnry2zP3w5AqE8o9/W4jwlJE/D28Da5OhEREWnu9p3Yx8tbX2Zz3mYAgr2Dua/Hfdze6XZ9VmkEFJJcFJIaH8MwWJuzlpnbZ5JRnAHo6oyIiIiYK/dULq9tf42lh5YC4G315q7OdzG9+3RCfEJMrk4ulEKSi0JS42Vz2FiUtojZO2efM8/3yb5PcnnU5SZXJyIiIs1BcWUxb+9+m08OfkK1oxqAG+Ju4JHej9AmsI3J1cnFUkhyUUhq/Mqry/lw/4e8u/ddd8eYwdGDebzv4yS2SDS5OhEREWmKquxVfHrwU97a/RYlVc7P0v1b9+fJfk/SpWUXk6uTS6WQ5KKQ1HScOH2CN3e/6e6EZ8HC2I5j1QlPREREao3DcPDtoW+ZtWOWe0/HjqEdebLvkwyKHoTFYjG5QvkjFJJcFJKanvN1wpvYeSLTu09XJzwRERG5JIZh8OORH5m5fSYHCg8AEOkXycO9H+bG+BvxsHqYXKHUBoUkF4Wkput8nfDu7XEvtyXdpu4yIiIicsH2Ht/LzG0z2ZS3CYAArwCmdZvG3V3uxs/Tz+TqpDYpJLkoJDVtNXXCe7T3o4yIHaFOeCIiIlKjzOJMZu2Y5Z6d4mX14rak27inxz2E+YaZXJ3UBYUkF4Wk5uF8nfA6h3Xm8T6Pc2WbKzV/WERERNwKyguYs2sOX6Z+id2wY8HCmPgxPNjrQaIDo80uT+qQQpKLQlLzcr5OeJe3vpzH+jxGj4geJlcnIiIiZiqpKmHe3nl8tP8jKuwVAFzV9ioe6/OYOuY2EwpJLgpJzVNhRSHv7HmHzw5+5t7T4Nr21/JI70eID403uToRERGpT5X2Sj498Cnv7H2H4spiAHpG9OSJvk/Qt1Vfk6uT+qSQ5KKQ1LwdOXWEObvm8FX6VzgMB1aLlRvjb+TBng8SFRhldnkiIiJSh+wOO1+lf8XsXbPJK8sDID4knkf7PMrV7a7WdPxmSCHJRSFJANKL0pm1YxarslcBzoWZt3e6nRndZ2hhpoiISBNjGAZrctbw2vbXSC9OB6CVfyse6vWQ2nk3cwpJLgpJcrZdBbt4dfurbMnbAjhbfE7uOplJXSYR4BVgcnUiIiLyR20/tp1Xtr3CzoKdAAR7B3NP93u4vdPt+Hr6mlydmE0hyUUhSX7pfJvFhfmGcW+PexmfOF57LImIiDRCBwsP8u8d/2bd4XUA+Hr4MrHLRKZ2m0qwtz4DipNCkotCktTEYThYkbWCf+/4N1klWQC0CWjDg70e5Ia4G3QrXkREpBE4VHyI13e+zvLM5QB4WDy4OeFmHuj5AJH+kSZXJw2NQpKLQpL8nmpHNYvTFjNn5xzyT+cDWtQpIiLS0P2yORPAyJiRPNjrQWJCYswtThoshSQXhSS5UBW2Cj49+Cnv7HmHkirn90yPiB480vsR+rfur7AkIiLSABw/fZy3dr/FgpQF2Bw2AIa2G8rDvR4mKSzJ5OqkoVNIclFIkotVUlXCe3vf48P9H7o3mrus9WU83Oth+rTqY3J1IiIizVNxZTHv7n2XTw584v753D+qP4/0foSeET1Nrk4aC4UkF4UkuVTHTx/nnT3v8Hny5+4NaQdGD+SRXo/QNbyrydWJiIg0D2XVZXyw/wM+2PcBp6pPAc6ZHo/2fpT+Uf1Nrk4aG4UkF4Uk+aPyyvJ4c/ebLEpdhM1w3ta/ut3VPNTrId3WFxERqSMVtgrmJ89n7p65nKw8CUBSiyQe6f0IV7W9StPg5ZIoJLkoJEltySnJ4Y3db7AkY4l7geiImBE80OsB4kLiTK5ORESkaai2V7MwbSFv7nrT3VApJjiGh3o9xPCY4VgtVpMrlMZMIclFIUlqW0ZRBrN3zXa3GrVarNwQdwP397yfdkHtTK5ORESkcbI5bHyd/jVv7X6Lw6cOAxAVEMUDPR9gTPwYPK2eJlcoTYFCkotCktSV5MJkXt/5Omty1gDgafHkpoSbuK/HfbQOaG1ydSIiIo2DzWFj6aGlvLHrDXJKcwBo6duSe3vcy7jEcdrkXWqVQpKLQpLUtT0Fe3h95+tsOLIBAC+rFxOSJjCj+wzC/cJNrk5ERKRhsjvsLD20lDd3v+ne1D3MN4ypXacyIWkC/l7+JlcoTZFCkotCktSX7ce2M2vHLLYe2wqAr4cvE5ImMLXbVIUlERERF7vDzrLMZbyx6w0ySzIBCPUJZWq3qdyedLvCkdQphSQXhSSpT4ZhsClvE7N2zGJ3wW7AGZbGJ41nWrdpCksiItJsOQwHyzOX88auN8gozgAgxCeEKV2ncGenOxWOpF4oJLkoJIkZDMNgw5ENzNk5h93HnWHJx8OH8YnOsBThH2FyhSIiIvXDYThYmbWSN3a9QVpRGgDB3sFM7jqZOzvdSaB3oMkVSnOikOSikCRmMgyDjUc2MnvXbPedJR8PH8YljmNat2lE+keaXKGIiEjdcBgOVmWvYs6uOaSeTAUgyDuISV0mcVfnuwjyDjK5QmmOFJJcFJKkITAMgx+P/MicXXPYWbATAG+rtzsstQpoZXKFIiIitcNhOPgu6zve2v0WySeTAQj0CuTuLnczsctEgr31eUzMo5DkopAkDYlhGPx09Cfm7JrDjvwdgDMs3ZJwC9O7T1frcBERabRsDhvLMpfx9u633WuOArwCmNh5Ind3uZsQnxCTKxRRSHJTSJKG6EyDhzk757A9fzvgbB1+S8ItzOg+Q2FJREQajWpHNUvSl/DOnnfILs0GIMgriLu63MXEzhMVjqRBUUhyUUiShswwDDbnbWbOrjlsO7YNcIalsR3HMq3rNNoFtzO5QhERkfOrslexKG0Rc/fM5UjZEcDZyntSl0nc3ul2rTmSBkkhyUUhSRqLLXlbmL1ztnufJavFysjYkczoNoOOLTqaXJ2IiIjTadtpvkj5gnl755F/Oh+Alr4tmdJ1ijaBlQZPIclFIUkam23HtvH2nrfZkLvBfeza9tdyT/d76Bre1cTKRESkOSurLmN+8nze3/c+hRWFAET6RzKt2zRuTbgVX09fkysU+X0KSS4KSdJY7Tuxj3d2v8N32d+5jw1oM4AZ3WfQr1U/LBaLidWJiEhzUVJVwqcHPuXDAx9SXFkMQHRgNNO7T2ds/Fi8PbxNrlDkwikkuSgkSWOXXpTO3D1zWXpoKXbDDkDvyN7c0/0eBkUPUlgSEZE6UVBewIcHPuTz5M8pqy4DoENwB2Z0n8HouNF4Wb1MrlDk4ikkuSgkSVNxuPQw8/bOY2HaQqod1QB0DuvMjO4zuLb9tXhYPUyuUEREmoKskizm7Z3HV+lfuX/edAztyD3d7+H6mOv180YaNYUkF4UkaWryy/P5YN8HfJ7yOadtpwGIDYllWrdpjI4djZeHruyJiMjF23diH+/ueZeVWSsxcH4e7B3Zm+ndpjO47WCsFqvJFYr8cQpJLgpJ0lQVVRTx8cGP+fjAx5RWlQLOBbQTO09kXOI4tV4VEZHfdWbfvnf3vMuPR390Hx/SdgjTuk2jT6s+JlYnUvsUklwUkqSpO1V1is9TPuej/R9RcLoAgECvQMYnjueuznfRKqCVyRWKiEhDY3fYWZ2zmrl75rLvxD4APCwejIwdydRuU0lskWhyhSJ1QyHJRSFJmosqexXfZHzDe/veI6M4AwBPqyejY0czpesU7bUkIiJU2atYkrGEeXvnkVmSCYCvhy83J9zM5K6TiQ6MNrdAkTqmkOSikCTNjcNwsP7wet7d+y7b87e7j1/V9iqmdp1K31Z91RFPRKSZKaooYn7yfD49+CknKk4AEOwdzB2d7uDOzncS5htmcoUi9UMhyUUhSZqzXQW7eG/ve6zKXuVehNs9vDtTu03lmnbXqEORiEgTl1mcyYf7P+Sr9K+osFcAzvWrk7pMYlziOAK8AkyuUKR+KSS5KCSJONu5vr/vfRanLabKUQVA+6D23N3lbm6MvxF/L3+TKxQRkdpiGAZbj23lg30fsO7wOvdFss5hnZncdTLDY4ZrjyNpthpkSLJYLC2A14AbXYe+Ah4xDKOohvFhwP8HDAfaAceBRcBfDcMovsD3VEgScTl++jifHvyUzw5+RkmV87wQ5B3EuIRx3NHpDqICo0yuUERELlW1o5qVmSt5f//77D+x3318SNshTO46mX6t+mm6tTR7DTUkfQu0Be51HXoLyDQMY0wN47vhDEnvAfuBDsAbwG7DMMZd4HsqJIn8Qnl1OQvTFvLxgY/JKc0BnF2NrutwHRM7T6RXZC+TKxQRkQtVWlXKFylf8PHBj8krywPAx8OHG+Nv5O4udxMbEmtyhSINR4MLSRaLpTPOoHOFYRibXMeuAH4EOhmGkXyBrzMe+AgIMAzDdgHjFZJEamB32Fmfu54P93/I5rzN7uM9wnswsctErutwnaZkiIg0UFklWXx28DMWpi2krLoMgDDfMO7odAcTkiaoGYPIeTTEkDQNeNkwjNBfHC8CnjAMY94Fvs4M4H8Nw4io4XkfwOesQ0HAYYUkkd+WXJjMRwc+4puMb6h2VAPOxb13dLqD8YnjCfEJMblCERFxGA42HtnIJwc+YX3uevfx+JB4JnWdxOi40fh4+PzGK4g0bw0xJD0HTDEMI/EXx1OAeYZh/O8FvEZLYDvwoWEY/13DmP8B/u8vjyskiVyY46ePsyB5AZ8lf0ZhRSHg3EPjxvgbuavzXcSFxplcoYhI83Oq6hSL0xfz2cHP3PsbAQyOHsydne9kYJuBWm8kcgHqLSTVFEp+4TKczRcmG4aR9IuvTwXmGobxj995n2BgBXASuNEwjOoaxulOkkgtqLJX8e2hb/lw/4ckn/x5Nmz/1v25rdNtXN3uajytniZWKCLS9GWVZPHpwU9ZlLbIPaUu0CuQmzrexO2dbqdDcAeTKxRpXOozJIUD4b8zLBO4k0ucbmexWIKA5UA5cINhGBUXUZ/WJIn8AWdayX64/0PWHV6Hw3AAzql44xPHMy5xHOF+v3cKEBGRC+UwHGzI3cAnBz/hh9wf3MdjgmO4s/Od3Bh/o/Y3ErlEDXG63ZnGDf0Nw9jsOtYf+InfaNzgCjnLgUpglGEY5Rf5vgpJIrXkyKkjLEhZwJepX7qn4nlaPRnWfhi3d7qd3pG9Nd1DROQSFVUUsTh9MQtSFpBVkgWABQtXtb2KOzvdyRVtrsBqsZpcpUjj1uBCErhbgLcB7nMdegvIOtMC3GKxRAOrgEmGYWx23UFaCfgDNwNlZ71cgWEY9gt4T4UkkVpWZa9ieeZy5ifPZ1fBLvfxxBaJ3JZ0GzfE3aANakVELoBhGOwq2MXnyZ+zPHO5e8PvQK9Abk64mTuS7qBdcDuTqxRpOhpqSArj15vJPnxmM1mLxRIDHAKuNgxjrcViGQqsqeHlYg3DyLyA91RIEqlD+0/sZ37yfJZmLKXC7pwJG+gVyNiOYxmfOJ740HiTKxQRaXhOVZ3im4xv+Dzlc1JOpriPdwrrxISkCYyOHa2LTSJ1oEGGJDMoJInUj+LKYhanLWZ+8nyyS7Pdx3tH9ubWhFsZHjMcP08/EysUETHfwcKDfJ78Od9kfEO5zbmCwMfDhxExI7gt6Ta6hXfTtGWROqSQ5KKQJFK/HIaDH4/8yPzk+Xx/+HvsrlmxQV5BjI4bzbjEcSSFJf3Oq4iINB3l1eWsyFrBguQF7D6+2308NiSWCYkTGBM/RnvRidQThSQXhSQR8+SX57M4bTFfpH5B7qlc9/Hu4d25NeFWRsaO1HQSEWmSDMNg9/HdLExdyLLMZe723Z5WT65rfx0TkibQr1U/3TUSqWcKSS4KSSLmcxgOfjr6E1+kfMHqnNXYHDYA/D39GRU3inEJ4+jSsos+LIhIo1dYUcjX6V+zMHUh6cXp7uPtgtpxS8It3NTxJm2bIGIihSQXhSSRhuXE6RN8lf4VX6R+4W5xC5DQIoGx8WMZHTdaHyBEpFGxO+xsOLKBRWmLWJOzxn0hyNfDl2EdhnFzws30bdVX7btFGgCFJBeFJJGG6cwmtQtSFrAqa5W77a2HxYNB0YMY23EsQ9oOwdvD2+RKRUTOL6ckh4VpC1mcvpj88nz38a4tu3JLwi2MjB1JkHeQiRWKyC8pJLkoJIk0fMWVxSzPXM7i9MXsLvh5UXOITwijYkcxtuNYuoRpOp6ImO/M+err9K/ZWbDTfTzEJ4Qb4m7g5o43qzmNSAOmkOSikCTSuGQUZ/BV2ld8nf41+ad/vjLbMbQjY+PHckP8DZqOJyL1qtpezfe537MkfQnrDq+j2lENgAULV0RdwS0Jt3BN+2t051ukEVBIclFIEmmc7A47Px39icVpi1mds5pKeyUAVouVK6KuYFTsKK5tfy2B3oEmVyoiTZFhGOwq2MWSjCUsy1xGcWWx+7mEFgmMiRvDqNhRtApoZWKVInKxFJJcFJJEGr+SqhKWZy5nUdqic6bj+Xj4MKTtEEbFjWJw9GBdxRWRPyynJIclh5awJH3JORtjR/hFMCp2FGPix2g6nUgjppDkopAk0rRkl2Sz9NBSvsn4hsySTPfxIK8ghsUMY1TsKPq16oeH1cO8IkWkUTl66ijLM5ezLHMZ+07scx/38/Tj2vbXMiZuDP2j+uu8ItIEKCS5KCSJNE2GYXCw8CBLDy1l6aGl53SWivCLYETsCK6PuZ4e4T3U8EFEfqWgvIAVWStYdmjZOQ0YrBYr/Vv3Z0z8GK5tf602vBZpYhSSXBSSRJo+h+Fg27FtLD20lBWZKyip+vmc1zqgNde1v84ZmCJ6aJ8SkWassKKQ77K+Y1nmMrbmbcXA+ZnHgoW+rfoyImYE13W4jpZ+LU2uVETqikKSi0KSSPNSZa9iQ+4Gvj30LesOr6PcVu5+LtIvkus6XMfwmOH0iuilqTMizcDx08dZnb2a77K+Y3PeZuyG3f1cz4iejIgZwfCY4UT6R5pYpYjUF4UkF4UkkearwlbBxiMbWZG1grU5aymrLnM/F+4XznXtnYGpT2QfBSaRJiSnNMcdjHYV7HLfMQLoHNaZkbEjuT7metoEtjGxShExg0KSi0KSiIDzDtPGIxtZmbWSNdlrKK0udT8X6hPKVW2v4pp213Blmyu1BkGkkTEMg9SiVFZlrWJV9iqSTyaf83z38O5c0/4ahnUYRofgDiZVKSINgUKSi0KSiPxStb2aH4/+yMqslazOXn3OGiZvqzdXtLmCoe2GMrTtUCL8I0ysVERqYnPY2FWwi3U561iVveqcdt0eFg/6terHNe2v4Zr219A6oLWJlYpIQ6KQ5KKQJCK/pdpRzY5jO1iTs4Y1OWvIPZV7zvPdw7tzdburGdpuKB1DO6pTnoiJiiuL+SH3B9YdXseG3A2/usAxIHoA17a/lqFthxLqG2pipSLSUCkkuSgkiciFMgyDtKI01uSsYW3OWvYc33PO89GB0QyKHsSg6EFc3vpyTcsTqWNnvifXHV7H+sPr2VmwE4fhcD8f4hPCoOhBXNPuGgZFD9L3pIj8LoUkF4UkEblU+eX5rDu8jjXZa9h0dBNVjir3c15WL/q06sOgNs7QFB8ar7tMIrWgtKqUzXmb2Zi7kfW56zladvSc5xNaJDCk7RCuansVPcJ7qOmKiFwUhSQXhSQRqQ3l1eVsztvMD7k/8EPuD7+altc6oDUD2wx03mWKupxgb51vRC6EzWFj7/G9/HjkRzYe2cie43vOadPtbfWmf1R/hrQdwuC2g9WRTkT+EIUkF4UkEalthmGQVZLlDExHfmBr3lYq7ZXu560WK13CunB51OX0j+pP78je+Hn6mVixSMOSU5rjDkWbj24+p9skQIfgDlwZdSUDowdqaquI1CqFJBeFJBGpaxW2CrYe28oPuT+wIXcDmSWZ5zzvZfWiZ0RP+kf154qoK+ga3hUvq5c5xYqYIPdULlvytrAlbwtb87ZypOzIOc8HewfTP6o/A9oM4Mo2VxIdGG1SpSLS1CkkuSgkiUh9yyvLY0veFn46+hObjm7iWPmxc5739/SnT6s+9G3Vlz6Rfega3hUfDx+TqhWpXYZhuEPR1mNbzxuKPC2e9IzsyZVRVzKgzQC6tOyitUUiUi8UklwUkkTETIZhkF2azaajm9h0dBOb8zZTVFl0zhhvqzfdwrvRO7I3fVr1oVdkL61pkkbD7rCTVpTGroJd7MzfydZjW3/VbMHT4knX8K5c1voyLmt1Gb0ie2kKnYiYQiHJRSFJRBoSh+Eg5WQKW/O2sj1/O9uPbedExYlzxliwkNAigd6RvekV2Yse4T1oF9RO3fOkQSipKmF3wW53KNpzfA9l1WXnjPG0eNItvBuXtb6Mfq370StCoUhEGgaFJBeFJBFpyAzDIKc0h23HtrEjfwfb87eTVZL1q3HB3sF0D+9O94judA/vTrfwboT5hplQsTQn1Y5q0k6msf/EfvYc38Ougl2kF6VjcO5nBX9Pf7pHdKdnRE/6tuqrUCQiDZZCkotCkog0NsdPH3cGpmPb2XN8DwdOHDhnj6YzogOj3YGpc1hnksKSCPEJMaFiaQqqHdVkFGWw78Q+9p/Yz77j+0g5mXLef3vtgtrRK6IXvSJ70TOiJx1DO2pNkYg0CgpJLgpJItLYVdurSSlKYU/BHvYc38Pe43vJKM4479iogCiSwpLoFNaJTi06kRSWRHRgtKbqyTnKqstIPZlKyskUUk6mcODEAQ4WHjxvIAryCqJLyy50Ce9CrwhnKGrp19KEqkVE/jiFJBeFJBFpikqrStl3Yh97CpyhKflk8q82uD0jyCuIxLBEElskEh8ST1xoHPGh8Zqu1wzYHDaySrLcgSj1ZCqpRam/+W+lc8vOdGnZha4tu9KlZRethxORJkUhyUUhSUSai5KqElIKU0g+mczBwoMkFyaTWpSKzWE77/gWPi2IC40jLsQZmuJC4ogNiSXSPxKrxVrP1csfUVxZTGZJJpnFmRwqPuR+nF2aTbWj+rxfE+kXSUKLBBJaJDjvFLkCkf7fi0hTppDkopAkIs1Ztb2ajOIMkk8mk3YyjfTidDKKMsg9lfurxfdn+Hj40DawLe2C29EuqB3tg9rTPqg97YLaERUYhafVs57/FmIYBicqTpB7Kpfc0lxyT+Vy+NRhMoszySzJpLCisMav9ff0p2OLjiSEOgNRYotEEkITCPUNrce/gYhIw6CQ5KKQJCLya6dtp8ksznSHpoziDNKL0jlcehibcf47T+Bs7dwqoBVRAVG0Dmjt/v3Mr6iAKIK8g+rxb9I0VNmryC/Pd/86Vn7MGYhcoehI2RFO207/5mtE+kcSGxxLTEgMMcExxIY4H0cFROnukIiIi0KSi0KSiMiFszlsHC07Sk5JDjmlOWSXZpNdms3h0sPklOZQaa/83dcI8Aog0j+Slr4tCfcLp6Vfy3Mfu/7cwrcFPh4+9fC3Mke1o5riymIKKwopqiiisLKQkxUnOVlx8pxAlF+ez8nKk7/7ehYsRPpH0jaoLdGB0bQNbEuH4A7uUKSW2yIiv08hyUUhSUSkdjgMB/nl+RwtO8rRU0c5WnaUvLI856/yPI6WHaW4sviiXtPHw4dg72DnL59gQrxDCPYJdh/z9/LHz9MPP08//D1dj7388PXwdR/39vDG0+qJh8UDL6sXHlaPi75zYhgGNsNGlb2KSnul+/dzHtsqKbeVU1pVSll1GaXVpZRVlXGq+tTPv6pOUVRZRGFFIaVVpRdVg7fVmwj/CFr5tyLSP5I2gW3cYSg6KJqogCi8Pbwv6jVFRORcCkkuCkkiIvWnvLqcvLI8Ck4XcOL0CU5UnOD46ePuxydOO38VVhT+5rS+P8qCBU+rp/OXxbmGyoEDwzAwMHAYDhzGuX+uaY3WH60j1CeUFr4tCPUJJcw3jBa+LYjwiyDy/7V3/yGS13Ucx5+vPXcv7ocdVGKeWJpl/hEqinGVZaVS/mGJgVoQgShmFhFZpBTZaSqUpiVKP4i0KKPAlH6ZEKUpghaZZP1hlqaXaZrnoXfe7r774zt7fW9vV3fmZuZ2dp8P+DKz3/18l/fu+zM785r5zHdW7bPTtm7lOs8iJ0kD1mtI8t24kqSerRpf1Zwxb91BLzhuuqbZsn0Lm7dtZvPzna11/eltT7P5+c08u/1Znpt8bqdt6+TWnb6eqqldfn5RbJ/ePu+Z3V7M+Ng4K1esZGLFBCtXrNxxffX4alaPr2bt+FpWT6xmzfiaZptYs+P6S1e+dEcY2ntibz9kVZKWAEOSJGngxjK2Y0nd7pquaSanJ5utJpmanmJyepKpmmL79HYmpycJIQljjDWXGduxJG8sY4QwsWKi2cYmDDaSpJ0YkiRJI2UsYzsCjiRJg+A5QiVJkiSpxZAkSZIkSS2GJEmSJElqMSRJkiRJUoshSZIkSZJaDEmSJEmS1GJIkiRJkqQWQ5IkSZIktRiSJEmSJKnFkCRJkiRJLYYkSZIkSWoxJEmSJElSiyFJkiRJklr22tMFDMrmzZv3dAmSJEmS9qBeM0Gqqs+l7FlJ1gP/3NN1SJIkSVo09q+qRxY6eCmGpAD7Ac/s6VoWgbU0gXF//HssV86B5c3+L2/2f3mz/8ub/d/ZWuDR6iL4LLnldp1ffsEpcSlr8iIAz1SV6w+XIefA8mb/lzf7v7zZ/+XN/u+i67+BJ26QJEmSpBZDkiRJkiS1GJKWtm3AhZ1LLU/OgeUyYLQoAAAFsklEQVTN/i9v9n95s//Lm/3fTUvuxA2SJEmStDt8JUmSJEmSWgxJkiRJktRiSJIkSZKkFkOSJEmSJLUYkiRJkiSpxZA04pKck+TBJFuT3JPkmBcZf0qSPyfZ1rk8eVi1ajC6mQNJzkxyW5KnOtutSY4eZr3qr27/B7SOOy1JJblx0DVqcHq4D1iX5OokmzrH3J/kxGHVq/7qof8fT/LXJM8leTjJFUleMqx61T9J3prk5iSPdv6Xv3cBx7ytM0+2JvlbkrOHUeuoMiSNsCSnAl8BLgaOAG4Dfp7kgHnGbwBuAK4HDutc/jDJG4dTsfqt2zkAHAt8H3g7sAF4CLglyfrBV6t+66H/M8e9CvhSZ7xGVA/3ARPAr4BXA+8DDgHOBB4ZRr3qrx76/wHgUprPzjkUOAM4FbhkKAWr31YDfwTOXcjgJAcCP6OZJ0cAXwSuSnLKwCoccX5O0ghLchfw+6r6cGvf/cCNVfWZOcbfAOxdVe9u7fsF8FRVnT6MmtVf3c6BOY5fATwFnFtV1w2uUg1CL/3v9Pw3wLeBY4B1VfWiz0Bq8enhPuBs4Dzg9VW1fXiVahB66P/XgEOr6p2tfV8Gjq6qBb0CrcUpSQEnV9W8KwOSXAacVFWHtvZdCxxWVRuGUObI8ZWkEdV5RvBI4JZZ37oFeNM8h22YY/wvX2C8FrEe58Bsq4Bx4Mk+lqYh2I3+fw54vKq+NajaNHg99v8k4E7g6iSPJbkvyfmd4KwR0mP/bweOnFlineQg4ETgp4OqU4vKfI8Bj0oyvgfqWfT22tMFqGcvB1YAj83a/xiw7zzH7NvleC1uvcyB2S6lWWpzax/r0nB03f8kb6ZZYnP4YEvTEPRy+z8IeAfwPZoHx68FrqZ5LPCFwZSpAem6/1X1gySvAG5PEpq+X1NVlw60Ui0W8z0G3ItmPm0aekWLnCFp9M1eL5k59u3OeC1+PfU0yaeA04Fjq2rrIArTUCyo/0nWAt8FzqyqJ4ZRmIaim9v/GPBv4KyqmgLuSbIfzRI8Q9JoWnD/kxwLXACcA9wFHAxcmWRTVW0cZJFaNOaaL3PtF4akUfYEMMWuzxjtw67PFMz4V5fjtbj1MgcASPJJ4HzguKq6dzDlacC67f9raN6wf3PzJDLQWXKdZBI4pKoeGEilGoRebv+bgO2dgDTjfmDfJBNV9Xz/y9SA9NL/jcD1VfXNztd/SrIa+HqSi6tqejClapGY7zHgJPCf4Zez+PmepBHVuTO7Bzh+1reOB+6Y57A75xh/wguM1yLW4xwgyXnAZ4F3VdXdg6tQg9RD//8CvIFmqd3MdhPw6871hwdWrPqux9v/74CDk7Tv+18HbDIgjZYe+78KmB2EpmheTciuw7XEzPcY8G5P5DI3X0kabZcD1ye5m2bynwUcAFwLkOQ64JHWWW6uBH6b5NPAT4D3AMcBbxl24eqbruZAZ4ndRuD9wN+TzDyrtKWqtgy7eO22Bfe/s6TyvvbBSf4LUFU77dfI6PY+4BrgozRLrL5K856k84Grhl24+qLb/t8MfCLJH/j/cruNwE2zXl3UCEiyhqaHMw5McjjwZFU9lOQSYH1VfbDz/WuBc5NcDnyD5kQOZ9Asu9ccDEkjrKpuSPIymrNVvZLmAdCJVfWPzpADaD1rVFV3JDkNuIjmH+MDwKlVdddwK1e/dDsHaNaiTwA/mvWjLgQ+P9hq1W899F9LSA/3AQ8nOQG4AriX5qQtVwKXDbVw9UUPt/+LaN57chGwHnicJjhdMLSi1U9H0awEmHF55/I7wIdo5sSOz8yqqgc7Hxx9BfAR4FHgY1X146FUO4L8nCRJkiRJavE9SZIkSZLUYkiSJEmSpBZDkiRJkiS1GJIkSZIkqcWQJEmSJEkthiRJkiRJajEkSZIkSVKLIUmSJEmSWgxJkiRJktRiSJIkSZKkFkOSJEmSJLX8D3hZFUnLfANkAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "n = 1\n", "L = 1\n", "E = ISW_energy(n, L)\n", "V = lambda x: 0\n", "res1 = solve_tise(E, V, 0, L, s=1, max_step=1e-3)\n", "res2 = solve_tise(E, V, 0, L, s=2, max_step=1e-3)\n", "res3 = solve_tise(E, V, 0, L, s=-1, max_step=1e-3)\n", "\n", "fig, ax = plt.subplots(dpi=100, figsize=(10, 5))\n", "ax.plot(res1.t, res1.y[0], label=\"s=1\")\n", "ax.plot(res2.t, res2.y[0], label=\"s=2\")\n", "ax.plot(res3.t, res3.y[0], label=\"s=-1\")\n", "x_axis(ax)\n", "ax.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As we can see, assuming we have the right energy, the initial energy only rescales the wave function. And it turns out that if you satisify the TISE and the boundary conditions, you only need to scale your solution by \n", "\n", "$$C = \\left(\\int_{-\\infty}^{\\infty} \\psi(x)^2 dx\\right)^{-1}$$\n", "\n", "to satisfy normalization.\n", "\n", "However, what if we do not know $E$? The choice of $E$ does matter, so an incorrect choice of $E$ might not satisfy the boundary conditions. In the example below, we solve the IVP but with the energy given perturbed a small amount from the actual energy." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.0005271889957662523\n", "0.001109764195982837\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "dE = .05\n", "res1 = solve_tise(E-dE, V, 0, L, max_step=1e-3)\n", "res2 = solve_tise(E+dE, V, 0, L, max_step=1e-3)\n", "\n", "print(res1.y[0, -1])\n", "print(res2.y[0, -1])\n", "\n", "fig, ax = plt.subplots(dpi=100, figsize=(10, 5))\n", "ax.plot(res1.t, res1.y[0], label=f\"$E=E_1-{dE}$\")\n", "ax.plot(res2.t, res2.y[0], label=f\"$E=E_1-{dE}$\")\n", "x_axis(ax)\n", "ax.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Instead of guessing the initial slope (which in general, any value will do), we can guess the energy. If $\\psi^{(E)}$ is a solution with $E$ as the energy, then we can rephrase the shooting problem as finding the roots of the function \n", "\n", "$$ g(E) = \\psi^{(E)}(L). $$\n", "\n", "In the example above, we have $g(E_1-0.05) = \\psi^{(E_1-0.05)}(L)=0.0027$ and $g(E_1-0.05)=\\psi^{(E_1+0.05)}(L)=-0.0015$. \n", "\n", "A simple root finding method for a continuous function (which we are assuming $g$ is) comes from the intermediate value theorem: if $f(a)$ and $f(b)$ have opposite signs, then there exists some $x$ such that $f(x)=0$. The bisection method takes advantage of this. Given a interval and a (continuous) function taking opposite signs at the end of the interval, the method calculates the function at the midpoint of the interval, checks the sign, and then updates the interval with this new midpoint so that the function still has opposite signs with the new interval, and repeating this until the interval is sufficiently small.\n", "\n", "From the example above, since $g(E_1-0.05)$ and $g(E_1+0.05)$ have opposite signs, we know that there exists a root within that interval (and of course, the root is at $E_1$). Let's see the shooting method in action now. Using the bisection method, we're going to need an inital energy range, so for simplicity, we'll just use the $[E_1-0.05, E_1+0.05]$ interval from above." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "actual energy: 0.12500000\n", "calculated energy: 0.12500038\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "E_shoot = shoot(E-dE, E+dE, V, 0, L)\n", "print(f\"actual energy: {E:.8f}\")\n", "print(f\"calculated energy: {E_shoot:.8f}\")\n", "\n", "res1 = solve_tise(E, V, 0, L, max_step=1e-3)\n", "res2 = solve_tise(E_shoot, V, 0, L, max_step=1e-3)\n", "fig, ax = plt.subplots(dpi=100, figsize=(10, 5))\n", "\n", "ax.plot(res1.t, res1.y[0], label=\"actual energy\")\n", "ax.plot(res2.t, res2.y[0], label=\"calculated energy\", ls=\":\", lw=5)\n", "x_axis(ax)\n", "ax.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As we can see, the calculated energy is very close to the original energy, and there is almost no difference in the solutions when using either energy.\n", "\n", "### Matching method\n", "\n", "The shooting method, however, will not be sufficient for other potentials. Let's see why with the finite square well. We'll be using the potential \n", "\n", "$$V(x)=\\begin{cases} -V_0 & -L \\leq x \\leq L \\\\ 0 & -L' \\leq x < L \\text{ or } L < x \\leq L'\\\\ \\infty & \\text{otherwise}\\end{cases}$$\n", "\n", "for the finite square well (only difference from class is the infinite height barrier at a distance $L'$ from the origin, keeping the particle in a finite domain). Let's set $V_0=1$, $L=1$, $L'=5$, and then see what a solution looks like with $E=-0.5$." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "L, Lp, V0 = 1, 5, 1\n", "V = lambda x: -V0 if abs(x) < L else 0\n", "res = solve_tise(-.5, V, -Lp, Lp, max_step=1e-3)\n", "\n", "fig, ax = plt.subplots(dpi=100, figsize=(10, 5))\n", "ax.plot(res.t, res.y[0], label=\"$E=-.5$\")\n", "i = np.where(res.t >= L)[0][0]\n", "ymin, ymax = res.y[0,:i].min(), res.y[0,:i].max()\n", "ymin, ymax = ymin-.1*(ymax-ymin), ymax+.5*(ymax-ymin)\n", "ax.set_ylim(ymin, ymax)\n", "x_axis(ax)\n", "hline(ax, [-L, L])\n", "ax.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the classically forbiden region (that is, where $V(x)>E$), the solution blows up due to numerical error. As the solutions in these regions are exponetial functions, the \"opposite\" exponential takes over (that is, instead of the decaying solution $e^{-\\alpha x}$, we get the increasing solution $e^{\\alpha x}$). However, note that the solution is correct in the classically forbidden region on the left, which is where we start solving from. What does the solution look like if we start solving from the right?" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "res1 = solve_tise(-.5, V, -Lp, Lp, max_step=1e-3)\n", "res2 = solve_tise(-.5, V, Lp, -Lp, max_step=1e-3)\n", "\n", "fig, ax = plt.subplots(dpi=100, figsize=(10, 5))\n", "ax.plot(res1.t, res1.y[0], label=\"solution from the left\")\n", "ax.plot(res2.t, res2.y[0], label=\"solution from the right\")\n", "i = np.where(res1.t >= L)[0][0]\n", "ymin, ymax = res1.y[0,:i].min(), res1.y[0,:i].max()\n", "ymin, ymax = ymin-.5*(ymax-ymin), ymax+.5*(ymax-ymin)\n", "ax.set_ylim(ymin, ymax)\n", "x_axis(ax)\n", "hline(ax, [-L, L])\n", "ax.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The solution from the right has the correct functional form, so we could \"splice\" the two solutions together to make a new solution. If we do this for this particular energy by taking the solution from the left all the way up to the classically beginning of the forbidden region on the right, and then taking the solution from the right, we get a discontinous solution, which does not satisfy the Schrodinger equations. However, if we change the energy to be close to an allowed energy..." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "E = -.6\n", "res1 = solve_tise(E, V, -Lp, Lp, max_step=1e-3)\n", "res2 = solve_tise(E, V, Lp, -Lp, max_step=1e-3)\n", "\n", "fig, ax = plt.subplots(dpi=100, figsize=(10, 5))\n", "ax.plot(res1.t, res1.y[0], label=\"solution from the left\")\n", "ax.plot(res2.t, res2.y[0], label=\"solution from the right\")\n", "i = np.where(res1.t >= L)[0][0]\n", "ymin, ymax = res1.y[0,:i].min(), res1.y[0,:i].max()\n", "ymin, ymax = ymin-.5*(ymax-ymin), ymax+.5*(ymax-ymin)\n", "ax.set_ylim(ymin, ymax)\n", "x_axis(ax)\n", "hline(ax, [-L, L])\n", "ax.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "the solutions \"match\", and so the spliced solution is continous. This is the essence of the matching method. We shoot from the left and right up to some matching point, which should happen before any divergent behavior for both solutions, and then aim to match the function and the derivative at that point. As a root finding problem, if $\\overrightarrow{\\psi^{(E)}}$ is a solution from the left and $\\overleftarrow{\\psi^{(E)}}$ is a solution from the right, both with energy $E$, and $x_m$ is the match point, then we want to find the root of \n", "\n", "$$g(E) = \\overrightarrow{\\psi^{(E)}}\\,'(x_m)-\\frac{\\overrightarrow{\\psi^{(E)}}(x_m)}{\\overleftarrow{\\psi^{(E)}}(x_m)} \\overleftarrow{\\psi^{(E)}}\\,'(x_m)\\quad,$$\n", "\n", "which will find the energy when the slope difference between the matched solutions is 0. For the matching method, we'll use the secant method, which is similar to Newton's root finding method, but we don't need to supply the derivative of $g$ (and is instead approximated). Below is a solution that we've matched." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "converged: True\n", "energy: -0.391453695424628\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "E = match(-.5, -.51, V, -Lp, Lp, 0)\n", "print(f\"energy: {E}\")\n", "\n", "x, psi = splice(E, V, -Lp, Lp, 0)\n", "\n", "fig, ax = plt.subplots(dpi=100, figsize=(10, 5))\n", "ax.plot(x, psi)\n", "x_axis(ax)\n", "hline(ax, [-L, L])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Direct matrix method\n", "\n", "The matching works well for general potentials, but we still need to search for the energy values. However, there is a method that can solve for the approximate energies directly, called the direct matrix method. Recall that we can write the TISE as \n", "\n", "$$\\hat{H}\\psi(x) = E \\psi(x)$$\n", "\n", "where $\\hat{H} = -\\frac{\\hbar}{2m}\\frac{d^2}{dx^2} + V(x)$. So finding the energies reduces to finding the eigenvalues of $\\hat{H}$. However, we'll need to discretize $\\hat{H}$ in order to use numerical methods for solving eigenvalues. By discretizing our domain into $N$ points as $x_j$ where $j ={0, 1, \\dots, N-1}$, we can use the central difference formula to approxmiate the TISE as\n", "\n", "$$-\\frac{\\hbar^2}{2m}\\frac{\\psi_{j+1} - 2\\psi_{j} + \\psi_{j-1}}{\\Delta x^2} + V_j\\psi_j = E\\psi_j + O(\\Delta x^2) \\quad \\text{for $j=1, 2, \\dots, N-2$} $$\n", "\n", "where $x_{j+1}-x_{j} = \\Delta x$, $\\psi_j = \\psi(x_j)$, and $V_j = V(x_j)$. Rearranging with $k = \\frac{\\hbar^2}{2m\\Delta x^2}$, $\\psi_0=0$, we have the following system of equations:\n", "\n", "\\begin{align}\n", "-k\\psi_2 + (2k+V_1)\\psi_1 &= E\\psi_1 \\\\\n", "-k\\psi_3 + (2k+V_2)\\psi_2 -k\\psi_1 &= E\\psi_2\\\\\n", "-k\\psi_4 + (2k+V_3)\\psi_3 -k\\psi_2 &= E\\psi_3\\\\\n", "\\vdots\\\\\n", "(2k+V_{N-2})\\psi_{N-2}-k\\psi_{N-3} &= E\\psi_{N-2}\n", "\\end{align}\n", "\n", "We can write this in matrix form, \n", "\n", "\\begin{align}\n", "\\begin{bmatrix}\n", "2k+V_1 & -k & 0 & \\dots & 0 \\\\\n", "-k & 2k+V_2 & -k & \\ddots & \\vdots \\\\\n", "0 & -k & 2k+V_3 & \\ddots & 0 \\\\\n", "\\vdots & \\ddots & \\ddots & \\ddots & -k \\\\\n", "0 & \\dots & 0 & -k & 2k+V_{N-2} \n", "\\end{bmatrix}\n", "\\begin{bmatrix}\\psi_1 \\\\ \\psi_2 \\\\ \\psi_3 \\\\ \\vdots \\\\ \\psi_{N-2} \\end{bmatrix} = E \n", "\\begin{bmatrix}\\psi_1 \\\\ \\psi_2 \\\\ \\psi_3 \\\\ \\vdots \\\\ \\psi_{N-2} \\end{bmatrix}\n", "\\end{align}\n", "\n", "or more compactly, $H\\psi = E\\psi + O(\\Delta x^2)$. Hence, we can approximate the eigenvalues of $\\hat{H}$ by finding the eigenvalues of the discretized Hamiltonian $H$. In practice, the eigenvalues accumlate error for the higher energy states, but for small enough energy states and the matching method, we can now solve for the $n$th exited state of arbitrary potentials.\n", "\n", "One system we can use to check our calculations is the quantum harmonic oscillator, whose analytic solutions are well known. Its potential is given by $V(x) = \\frac{1}{2}m\\omega^2x^2$, and its energy levels are $E_n = \\hbar\\omega (n+\\frac{1}{2})$. Using the direct matrix method and letting $\\omega=1$, $m=1$ and $h=1$, the plot below shows the difference between the analytic and diect matrix method. We can see that increasing the subdivision (and thus decreasing $\\Delta x$) increases the accuracy of the estimate." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "V = lambda x: 1/2*x**2\n", "Es100 = solve_energies(V, -Lp, Lp, n=100)\n", "Es1000 = solve_energies(V, -Lp, Lp, n=1000)\n", "ns = np.arange(0, 25)\n", "\n", "fig, ax = plt.subplots(dpi=100, figsize=(10, 5))\n", "ax.scatter(ns, hbar*(ns+1/2), label=\"analytic energy\", s=100)\n", "ax.scatter(ns, Es100[ns], label=\"direct matrix energy with 100 subdivision\")\n", "ax.scatter(ns, Es1000[ns], label=\"direct matrix energy with 1000 subdivisionsb\", marker=\"P\", color=\"pink\")\n", "ax.set_xlabel(\"energy level\")\n", "ax.set_ylabel(\"energy\")\n", "ax.set_xticks(ns, minor=True)\n", "ax.grid(alpha=.25)\n", "ax.grid(alpha=.25, which=\"minor\")\n", "ax.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using the energies from the direct matrix method, below are some of the excited states for the quantum harmonic oscillator." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, axs = plt.subplots(3, 3, dpi=100, figsize=(12,12))\n", "for i in range(9):\n", " E = Es1000[i+5]\n", " x, psi = splice(E, V, -Lp, Lp, .1)\n", " axs[i//3][i%3].plot(x, psi)\n", " axs[i//3][i%3].set_title(f\"{i+5}th excited state\")\n", " tp = np.sqrt(2*E)\n", " hline(axs[i//3][i%3], [-tp, tp])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Returning to the finite square well (with the same parameters from above), below are some of the wave functions for the higher excited states. Notice that after the 6th excited state, there is enough energy for the solution the classically forbidden region to be oscillatory." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "energy of the final bound state: -0.1422\n", "energy of the first unbound bound state: 0.0071\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "V = lambda x: -V0 if abs(x) < L else 0\n", "Es = solve_energies(V, -Lp, Lp, n=1000)\n", "fig, axs = plt.subplots(3, 3, dpi=100, figsize=(12,12))\n", "for i in range(9):\n", " x, psi = splice(Es[i+4], V, -Lp, Lp, L)\n", " axs[i//3][i%3].plot(x, psi)\n", " axs[i//3][i%3].set_title(f\"{i+4}th excited state\")\n", " x_axis(axs[i//3][i%3])\n", " hline(axs[i//3][i%3], [-L, L])\n", " \n", "print(f\"energy of the final bound state: {Es[5]:.4f}\")\n", "print(f\"energy of the first unbound bound state: {Es[6]:.4f}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solving the time-dependent Schrodinger equation\n", "Recall that the time-dependent Schrodinger equation (TDSE) is.\n", "\\begin{align}\n", "i h \\frac{\\partial}{\\partial x} \\psi (x,t) = \\hat{H} \\psi\\\\\n", "\\end{align}\n", "\n", "where $\\hat{H}=-\\frac{\\hbar^2}{2m}\\nabla^2 + V$ is the Hamiltonian operator, representing the total energy of the system.\n", "\n", "This PDE is quite daunting until one applies seperation of variables to discover that the time evolution of the Schrodinger equation is just the product of the TISE and a phase term $e^{-i\\hat{H}t/\\hbar}$, giving you a solution to the TDSE.\n", "\n", "However, this isn't always that useful in practice, as evolving forward the eigenstates of the time-independent solution is useful in the context of certain contexts and potentials, such as solving the TISE in an infinite square well. But for arbitrary initial conditions, while the particle will eventually settle into the time independent steady state solution, we can say very little about the transient solution (going from initial conditions to the steady state), particularly if the potential is non-linear. \n", "Further, our entire assumption of seperability goes out the window if the potential is time varying.\n", "\n", "This clearly poses a problem, as there are certainly intresting problems we might want to model, such as how a electron settles into a bond orbital, as this could effect the initial stability of a chemical compound during bonding, or the dynamic interaction of multiple particles in a system. However, our current tools provide little to nothing of use to these problems.\n", "\n", "### Numerical methods\n", "This is where the numerical solutions of the TDSE become quite useful. The construction of the Schrodinger equation easily emits a formula for the time derivitive of $\\psi$ at any given point. Thus, given a initial condition of the system, we should be able to solve this as a simple discretized finite differences (computing derivitives locally from a discretized domain) problem. However, we run into some complications. For one, we know that the actual function of the time evolution we are approximating is a complex exponential ($e^{-iH\\Delta t/\\hbar}$) for every time step, which is inherently unstable because any small purterbation to the real part will cause an exponenital difference in the output. This is a problem because second order finite differences methods (such as Runge-Kutta) is generally our go to tool for time evolution of states. However, the idea is still attractive because over very small time horizons, we can treat our potential as constant in time and also treat the current state of $\\psi$ as the solution to some TISE which is being time evolved with our simple phase term. Because we are multiplying by each exponential at each timestep, and products of exponentials are a exponential of the sum of the exponential terms, this should still work out to being the correct time evolution.\n", "\n", "In numerical analysis, when a system is particularly siff, such as some propogations of the Schrodinger equation, we often try and solve this with a implicit method, where we solve a optimization problem to find the most likely next state by estimating what the derivitive will be at the next state, and then steping backwards in time from there to try and find our current state. Instability is only in one direction of time, thus, because this effectively solves backwards in time, it will be stable for any unstable problem. Indeed, a version of this is often used for time evolving the Schrodinger equation, in a approximation known as the Crank-Nicolson Approximation, which is always stable in both forward and backwards time. However, these optimization problems often emmit numerically unsuitable solutions which degrade the accuracy of the solution.\n", "\n", "So far, the quest for TDSE evolution in arbitary potentials is grim, while our discretized exponential is theoretically sound, our forward propogation is either unstable in space or time. However, we do know some things about the actual quantum mechanics at the heart of all of this math. For one, momentum is quantized discretely for any true solution of the Schrodinger equation. And in our simulation, because space is quantized discretely, so is the potential. The crux of our problem is really the Laplacian term in the Hamiltonian, because our approximations of spacial derivitives are inaccurate, making all of our solutions unstable. If there was some way of relating functions in space to functions of momentum, and then a easy way to take a derivitive which would not rely on a finite differences approximation. \n", "\n", "### Split-step operator method\n", "Fortunately for us, the Fourier transform does just this, and the fast Fourier transform (FFT) is a very efficient and accurate way of computing this on a computer. The Fourier transform allows us to transform into momentum (phase) space and operate on the function from there. In phase space, derivitives are taken by multiplying by the phase variable times $i$. This makes it extremely easy to find the Laplacian in phase space as one simply has the multiply by $-k$. Because the Fourier transform accounts for the function at all points at once going into phase space, this same operation with the fast Fourier transform can be thought of as a high order approximation of the Laplacian which global convergence as the the number of quantized momenta grows large. What is better, is that in quantum mechanics, we have one expected wavenumber along with some uncertainty surrounding it. Because this is proportional to momentum, we know that, in momentum space, the function we are operating on will be quite simple, and conserving the wave number through steps should be trivial for the Fourier transform. By taking the Laplacian with the Fourier transform and applying the locally time independent potential assumption, we have stumbled on a variation of the split-step operator method, a spectral method for integrating the TDSE in time. \n", "\n", "\\begin{align}\n", "\\psi(x, t + \\Delta t) = e^{-iV(x,t) \\Delta t /2\\hbar} \\mathbb{F}^{-1} [ e^{-ik^2 \\Delta t / 2m\\hbar}\\mathbb{F}[\\psi(x,t)]] + O(\\Delta t^2)\n", "\\end{align}\n", "\n", "For certain solutions, Strang splitting can also be applied to further improve performance. \n" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "class TDSE_sim:\n", " def __init__(self, initial_position=0.0, uncertainty=0.5, wavenumber=40.0, domain=10.0, wavepacket_scaling=0.5, spacial_resolution=2**10, dt=1e-4, sim_length=1.0):\n", " self.spatial_res = spacial_resolution\n", " self.dt = dt\n", " self.num_timesteps = int(sim_length/dt)\n", " self.domain = domain\n", " \n", " # allow for periodic boundary conditions\n", " self.x = np.linspace(-self.domain/2, self.domain/2, num=self.spatial_res+1)[0:-1]\n", " self.k = 2*np.pi/(2*self.domain) * np.arange(-self.spatial_res/2, self.spatial_res/2)\n", " self.dx = self.x[1] - self.x[0]\n", " \n", " self.psi = (np.exp(-(self.x - initial_position)**2 /(4 * uncertainty**2)) * np.exp(1.0j * wavenumber * self.x))/((2 * np.pi * uncertainty**2)**(1.0/4))\n", " self.V = np.zeros_like(self.x)\n", " \n", " self.total_energy = []\n", " self.total_energy_timesteps = []\n", " \n", " def stepn(self, n):\n", " for i in range(n):\n", " psi_phase = np.fft.fftshift(np.fft.fft(self.psi))\n", " if i == 0:\n", " self.total_energy.append( np.abs(np.sum( np.fft.ifft(np.fft.ifftshift(psi_phase* 2*self.k)) + self.V )))\n", "\n", " # Kinetic Term\n", " psi_phase = np.exp(self.dt * -1.0j * (self.k**2)/2) * psi_phase\n", " psi = np.fft.ifft(np.fft.ifftshift(psi_phase))\n", " # Potential Term\n", " self.psi = np.exp(-1.0j * self.dt * self.V) * psi\n", " if len(self.total_energy_timesteps):\n", " self.total_energy_timesteps.append(self.total_energy_timesteps[-1] + n * self.dt)\n", " else:\n", " self.total_energy_timesteps.append(0)\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example 1: Infinite square well aproximation\n", "For a first experiment, we revisit the infinite square well, where we approximate a infinite square well with a continuous, piecewise function which grows extremely large after a certain point. We use this continuous function to ensure that the laplacian will be well defined for every point on the domain which helps with stability of the simulation. This is why it will appear that the wave part of $\\psi$ extends too far into the well wall.\n", "\n", "We get our initial conditions from the wavepacket solution to the TISE with a given wave number. For the purposes of numerical stability, $\\hbar =1$. \n", "\n", "The following sims are run with a wavenumber of 5 and 40 to compare the output. The top plot represents the wave function and the potential, with the blue line being the real part and the orange line being the imaginary part. The bottom plot represents the magnitude of the wave function squared (that is, the probability density)." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "sim = TDSE_sim(wavenumber=5, domain=20)\n", "# infinite potential well\n", "sim.V[sim.x < -8] = 1e3* (sim.x[sim.x < -8]+8)**2\n", "sim.V[sim.x > 8] = 1e3*(sim.x[sim.x > 8]-8)**2" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Video('infinite_square_well.mp4')" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "sim = TDSE_sim(wavenumber=40, domain=20)\n", "\n", "# infinite potential well\n", "sim.V[sim.x < -8] = 1e3* (sim.x[sim.x < -8]+8)**2\n", "sim.V[sim.x > 8] = 1e3*(sim.x[sim.x > 8]-8)**2" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Video('infinite_square_well2.mp4')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As we can see, near the end of the sim, the particle is settling into the expected phase shifted TISE solution where it has a collection of places where it is 0 probability dependent on the wave number. In addition, because the well is much wider then the initial width of the particle, its energy level drops dramatically, but due to conservation of energy, its momentum goes up proportionally to account for this, resulting in the much higher wave number of the steady state solution then what we set in the initial conditions.\n", "\n", "We can talk all day about the second order accuracy of the split-step method, but a much more compelling argument for the accuracy of our sim is in the conservation of energy in the Hamiltonian. Below, we present a graph showing the ratio of the total energy at a given second to the initial total energy of the particle. We see through the whole simulation that the Hamiltonian remains constant." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.99, 1.01)" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(sim.total_energy_timesteps, np.array(sim.total_energy)/sim.total_energy[0])\n", "ax = plt.gca()\n", "ax.set_ylim(0.99, 1.01)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Example 2: Tunneling in a well" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "sim = TDSE_sim(initial_position=-5, wavenumber=5, domain=20)\n", "\n", "# infinite potential well\n", "sim.V[sim.x < -8] = 1e3* (sim.x[sim.x < -8]+8)**2\n", "sim.V[sim.x > 1] = 16.625 + 5\n", "sim.V[sim.x > 1.3] = 0\n", "sim.V[sim.x > 8] = 1e3*(sim.x[sim.x > 8]-8)**2\n" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Video('tunneling_in_well.mp4')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Example 3: Double Potential Well" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "sim = TDSE_sim(initial_position=-5, wavenumber=10, domain=20)\n", "\n", "# infinite potential well\n", "E_naut = 1.0\n", "sim.V = 1.0*( 0.01* (1.3*sim.x)**4 - (1.3*sim.x)**2) +(16.625 + 8)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Video('double_potential_well.mp4')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References\n", "\n", "* Izaac, Joshua, and Jingbo Wang. Computational quantum mechanics. Springer International Publishing, 2018.\n", "\n", "* Hermann, Mark R., and J. A. Fleck Jr. \"Split-operator spectral method for solving the time-dependent Schrödinger equation in spherical coordinates.\" Physical Review A 38.12 (1988): 6000.\n", "\n", "* Griffiths, David J., and Darrell F. Schroeter. Introduction to quantum mechanics. Cambridge University Press, 2018.\n", "\n", "* https://math.mit.edu/~stevenj/fft-deriv.pdf\n", "\n", "* http://cacs.usc.edu/education/cs653/03-1SpectralQD.pdf\n", "\n", "* https://kitchingroup.cheme.cmu.edu/blog/2013/02/26/Derivatives-by-FFT/" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 2 }