├── LICENSE
├── README.md
├── animations
├── PIB_TimeEvolution.gif
└── Pendulum.gif
├── img
└── NumQM.png
├── notebooks
├── NumQM_Basic_01.ipynb
├── NumQM_Basic_02.ipynb
├── NumQM_Basic_03.ipynb
├── NumQM_Basic_04.ipynb
├── NumQM_Basic_05.ipynb
└── NumQM_Basic_06.ipynb
└── pdf
└── NIUS30Dec2021_NumQM.pdf
/LICENSE:
--------------------------------------------------------------------------------
1 | MIT License
2 |
3 | Copyright (c) 2021 Raghu
4 |
5 | Permission is hereby granted, free of charge, to any person obtaining a copy
6 | of this software and associated documentation files (the "Software"), to deal
7 | in the Software without restriction, including without limitation the rights
8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
9 | copies of the Software, and to permit persons to whom the Software is
10 | furnished to do so, subject to the following conditions:
11 |
12 | The above copyright notice and this permission notice shall be included in all
13 | copies or substantial portions of the Software.
14 |
15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
21 | SOFTWARE.
22 |
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/README.md:
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1 | The best way to use this material is by forking it by click the Fork button at the top, right corner. Then you will get your own copy to play with!
2 |
3 | The presentation and the notebooks are prepared for the lecture Numerical Approaches for Quantum Mechanics on 30 December 2021 as a part of the program
4 | [National Initiative on Undergraduate Science (NIUS)](https://nius.hbcse.tifr.res.in/). NIUS is an initiative of the [Homi Bhabha Centre for Science Education, TIFR](https://www.hbcse.tifr.res.in/).
5 |
6 | Click the slides below for the presentation
7 | 
8 |
9 |
10 |
11 |
12 | You can access the Ipython notebooks interactively at [https://mybinder.org/v2/gh/raghurama123/NumQM_Basic/HEAD
13 | ](https://mybinder.org/v2/gh/raghurama123/NumQM_Basic/HEAD)
14 |
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/animations/PIB_TimeEvolution.gif:
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https://raw.githubusercontent.com/raghurama123/NumQM_Basic/59286ff3c7339f3c8055ff60200e04f021b187aa/animations/PIB_TimeEvolution.gif
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/animations/Pendulum.gif:
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https://raw.githubusercontent.com/raghurama123/NumQM_Basic/59286ff3c7339f3c8055ff60200e04f021b187aa/animations/Pendulum.gif
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/img/NumQM.png:
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https://raw.githubusercontent.com/raghurama123/NumQM_Basic/59286ff3c7339f3c8055ff60200e04f021b187aa/img/NumQM.png
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/notebooks/NumQM_Basic_01.ipynb:
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1 | {
2 | "cells": [
3 | {
4 | "cell_type": "markdown",
5 | "id": "3606c937",
6 | "metadata": {},
7 | "source": [
8 | "# Particle-in-a-box wavefunctions"
9 | ]
10 | },
11 | {
12 | "cell_type": "code",
13 | "execution_count": 1,
14 | "id": "f76422a0",
15 | "metadata": {},
16 | "outputs": [
17 | {
18 | "data": {
19 | "image/png": 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+QSK+OPw3p3T4r7+bMxaSDkGfjz2yiPyZmsGTMzYzaPIqwkIC+W5UCx7vWtN1k/yVaQSdnoEdP8Laz1xzDOVUBUODeLZHbb4Z1owsY7j1wxW8+OM2UtJ1qLCn0kLiSzZ9C5u+gbb/hnJ5H9LnbCv3nqTLO4v5evVB7mlVkTmjW9PQHdfBm90HldrDL49D4h+uP55yiqaVivPLg20Y2LQcHy/dx03jl7D+4Gm7Y6lseHQhEZFPRCRBRLZc4X0RkfEisltENolII3dn9Bin91tzaJVtBq0fsTvN36RmZPLCj9voP2klASJMG9Gcp26uRViwm6YaDwiw1nwPzmetApmR6p7jqjwrEBrEi7fU5b9Dm5KankWfD5bz2i87SHfTRJD+eOn/es7ZowsJ8BnQ5SrvdwWqOh7DgQ/ckMnzZGZYKxwC9J4EgZ4zGG93wjlueX85k5fu447m5fn5wda2XO+mUJQ1kuvYJpj3vPuPr/KkVdUS/PJQa/rGRDNh4R76TlzBgZN/uvSYYWFhnDx50q+KiTGGkydPEhaWuwEvnvMTJxvGmMUiUuEqm/QEvjDWd3qliBQRkShjzFH3JPQQS8bBoVXQ+2NruVwPYIzhmzWHeO6HreQPCeKTIbF0qFHS3lA1boLYu2HFe1Clo8ffW6P+LjwsmNf61qdd9Uge+24T3cYv5YVbatOrYbRLjhcdHU18fDyJiYku2b+nCgsLIzo6d3+nHl1IcqAMcOiSr+Mdr11WSERkOFarhXLlyrklnFscXAmLXoV6/aFeP7vTAHDmfBqPf7+Zn7cco1WVErx5a30irzW9ibt0fgn2L4MZo2DUcihQ3O5EKpduqhtF/bJFeOib9Tw8dSOL/zjB8z1rE+7kpZSDg4OpWLGiU/fpqzz90pbTGGMmGWNijTGxERERdsdxjpQk64a7IuXgpsvvbLXD6n2n6PrOEn7bdpzHu9bgi7ubeE4RAQjJD30nw4VTMPt+a5i08jpliuRjyrBmPNSpKrM2HKbb+KVsOHTG7lh+y9sLyWGg7CVfRzte8w+/PgVnD1uXtMLyPl9OXmRlGSYs3E3/SSsIDQrg+3tbMKJt5eub4sTVStWFTs/CzjmwcYrdadR1CgoM4KFO1Zg6ojmZWYZ+E5fz2bJ9ftWn4Sm8vZDMBu5wjN5qBiT5Tf/I/qWw7gtofh+UbWxrlKTz6Qz7Io7XftnJTXWj+HF0a+pFF7E10zU1HQVlm8LcJyDZv66B+5rGFYoxZ3Rr2laL4NkftnH/1+s5l5Judyy/4tGFRESmACuA6iISLyJDRWSkiIx0bDIH2AvsBj4C7rUpqnulp1jTpBetAO0etzXKpvgzdHt3CYt3JfJcj9q8O6AhBUO9oOstIAC6j4fUZJhr79+hyrvC+YOZNDiWx7rW4OctR+n53jJ2HDtrdyy/4dH/440xA67xvgHuc1Mcz7FkHJzcDYNnWNf8bWCM4atVB3n+h21EhIcybURz99xc6EyRNaD1mP8NVqjaye5EKg8CAoSRbSvToGwRHpiynlveX8Z/etWldyPXjOpS/+PRLRKVjePbYOlbUH+AbcNXL6RlMmbaRp6auYUWVYrz4wOtvK+IXNT6X9ZU8z89DGmuvS9BuUezSsX5aXQrGpQtwphpG3n8+82kZuj0Kq6khcSbZGXCD6OtGW07v2RLhPjT5+nzwXJmbjjMmBuq8cmdjSlaIMSWLE4RFGpd4jpzEBb8x+40ykkiw8P479CmjGpXmSmrDzJg0koSzuryy66ihcSbxH0C8Wvgxpdtuf9hxZ6T9HhvGYdOn+eTOxszumNVzxyVlVvlm0PMXbByAhxZb3ca5SRBgQH8u0sNJgxsxI5j57j53aU6V5eLaCHxFkmHrRX/KneEere69dDGGD5fvp9Bk1dRNH8ws+5rSfsakW7N4HKdnoUCkTB7tDXljPIZN9WN4vt7WxAaHMBtH65kWtyha39I5YoWEm9gDMx5BLIy4OY33bqmRkp6Jo9O38Qzs7fSvnoEM+9rSaWIgm47vtvkKwI3vWbNxbXyfbvTKCerUaoQs+9rReOKRa1/z7O2uG3iR3+ghcQbbJ9t3TzX/glryK+bJJxNof+klXy7Np7RHaowaXCs06eh8Cg1e0D1brDgZWs2ZeVTihYI4fO7mnBPq4p8vuIAgz5exak/0+yO5RO0kHi6tPMw90koWReaue82mW1HznLL+8vYeewcHwxsxJjO1X2jP+RqRKypZiTA+jtXPicoMICnbq7Fm7fWZ/3BM/SasIzdCcl2x/J6Wkg83fLx1oqHXV912/Twv287Tt+Jy8ky8O3I5nStG+WW43qEwmWgzb+sFRX3LrQ7jXKR3o2imTK8KckpGfSesIxlu0/YHcmraSHxZGcOwdK3oXYvqNDS5YczxvDxkr0M+zKOyhEFmXV/S+qUKezy43qcZvdZlxB/fkw73n1YTPlizLyvJaUKh3HnJ6uZsvqg3ZG8lhYST/bb04CBG15w+aHSM7N4YsYWXvxpOzfWKsW0Ec0p6Umz9rpTcJh1n07idmvItfJZZYvl57tRLWhZpQSPf7+ZF3/cRmaWTvqYW1pIPNWB5bD1e2j5EBQpe83N8yLpQjpDPrV+I7u3XWUmDGxEvhA3LYPrqWp0g4ptYcFLcP6U3WmUC4WHBTP5zliGtKjAx0v3MeLLOP5M1ZZobmgh8URZmfDzo1AoGlo+6NJDHT5zgX4Tl7N63ynG9avPo11q+H6nek6IQJdXIPWcVUyUTwsKDODZHrV5oWdt5u9IoP+klSSc0zvhc0oLiSda9wUc2wydn3fppIxbjyTRe8Iyjp5J4fO7mtA3Rie3+5uStaDxUOvy1rEtdqdRbjC4eQU+vjOW3QnJ9J6wXEd05ZAWEk9z4QzMfwHKtYDavV12mCW7Erntw5UEiDB9VAtaVCnhsmN5tXaPW3Ob/fKYrqboJzrUKMnUEc1ISc+kzwfLWbNfL21eixYST7PoVeuafNdXXHYH+7dxh7jr0zVEF83HjHtbUr1UuEuO4xPyF4P2T8L+JdaNocov1IsuwvejWlK8QAgDP17FT5v8Y72866WFxJMk7oTVkyDmToiq7/TdG2N45/ddjJ2+ieaVi/PtyOaUKuynI7NyI+YuiKxtLW2cfsHuNMpNyhW3RnTVK1OY+75ex0eL9+oyvleghcST/PoUBBeADv/n9F1nZhmemLGFt37/gz6NovlkSGPfnu7EmQKDrBbimYPWDMHKbxQtEMJ/72nKTXVL8dKc7bz003aydHjwZbSQeIp9S2DXr9aKfQWc21+Rkp7JvV+t/Wt477h+9QgO1G99rlRsA9W6WjeI6nBgvxIWHMh7Axr9NTz4X99u1Akf/0F/mngCY+D3Z6BQGWg6wqm7PpuSzp2frGbu1uM8070Wj3apgbhx9mCf0ukZSEuGxePsTqLcLCBAeKZ7LcbeWJ0Z6w8z7Is4zqfpvSYXaSHxBNtmwuG11uy+wfmcttuEsync9uFK1h08zTv9G3BXy4pO27dfiqwJDW6HNR/B6QN2p1FuJiLc174Kr/Suy+I/Ern9o1Wc1tmDAS0k9stMh3nPQ0RNax12J9l/4k/6TFzOgZN/MvnOxvRsUMZp+/Zr7Z6wZgfWmxT9Vv8m5fhgUAzbjp6l78TlHD6jAzC0kNht7Wdwaq+1Ql+Ac6Yl2XI4ib4Tl5OcksHXw5rRplqEU/arsGYHbjoSNk2Do5vsTqNscmPtUnx5dxMSzqXS94Pl7E44Z3ckW2khsVPqOeu+kfItodqNTtnlmv2nGDBpJSGBAUwf1YIGZYs4Zb/qEq0etm5S/P1Zu5MoGzWtVJxpI5qTkWXoN3EFm+OT7I5kGy0kdlrxPvyZCJ2ec8rNhwt3JjB48ioiCoUyfVQLKvvikrieIF8RaPMI7Jmna5b4uZpRhfh2RHPyhwQx4KOVrNp70u5IttBCYpfkBFg23lretWzjPO/up01HGfZFHJVKFGTaiOaULuK8TnuVjcbDoHBZ+O0ZyNKhoP6sQokCfDeqBaUKh3HHJ6tZsCPB7khup4XELotehYwU6PhMnnc1dc1BHpiyjgZlizBleDNKFAx1QkB1VcFh0OEpOLrBmu5f+bVShcOYNqI51UqGM+yLOH7YeMTuSG7l0YVERLqIyE4R2S0ij2Xz/hARSRSRDY7HPXbkzLWTe6xO9pg7oUSVPO3q4yV7+fd3m2ldNYIv7m5K4Xx6t7rb1O0HJetYk2xm6DBQf1esQAhfD2tKo/JFGf3Ner5e5T8rLnpsIRGRQOB9oCtQCxggIrWy2XSqMaaB4/GxW0Ner/kvQGAItL2sNuaYMYa3fvuDF3/aTre6UXx0R6wuRuVuAYFW/9bp/dYvBsrvhYcF88XdTWhXLYInZmzmo8V77Y7kFh5bSIAmwG5jzF5jTBrwDdDT5kx5d2wzbJ0BzUZBeMnr2oUxhld+3sE783bRLyaa8QMaEhLkyd9KH1alI5RvBUvGQdp5u9MoDxAWHMiHg2PpVi+Kl+ZsZ/y8XT4/2aMn//QpAxy65Ot4x2v/1EdENonIdBG54pq0IjJcROJEJC4xMdHZWXNuwX8gtDC0eOC6Pp6VZXhm9lY+XLyXO5qX59U+9QjUFQ3tIwIdnoTk47DGOxrEyvVCggIY378hfRpF8+Zvf/Da3J0+XUw8uZDkxA9ABWNMPeA34PMrbWiMmWSMiTXGxEZE2HSDXvxa2DnHKiL5iub645lZhn9/t4kvVhxgRJtKPNejti6L6wnKt4DKHWHpW9a9QUoBgQHC633rMbBpOT5YuIfnftjmszMHe3IhOQxc2sKIdrz2F2PMSWNMquPLj4EYN2W7PgtegnzFoNnIXH80PTOLh6Zu4Nu18TzYsSqPddXJFz1KhyfhwilYNdHuJMqDBAQIL95Sh6GtKvLZ8v08MWMzmT5YTDy5kKwBqopIRREJAfoDf1uiTkSiLvmyB7Ddjfly58By6wa2Vg9DaO5WJEzNyOS+r9bxw8YjPNa1Bg/fUE2LiKcpEwPVu8Gyd+HCabvTKA8iIjzVrSYPdKjCN2sO8a9pG8jwsWnoPbaQGGMygPuBuVgFYpoxZquIPC8iPRybjRaRrSKyERgNDLEn7TUYA/NfhIIloXHuRiinpGcy8su1/LrtOM/1qM3ItpVdFFLlWfsnIDXJmrFAqUuICP/qXJ2xN1Zn5oYjjP5mvU+taRJkd4CrMcbMAeb847WnL3n+OPC4u3Pl2t6FcGAZdH0NQvLn+GMX0jIZ/mUcS3ef4OXedRnQpJzrMqq8K1UHaveClR9YEzs6eYEy5f3ua1+F0KAAXvxpOxmZ63jv9kY+MeLS+8/A011sjRSKhpghOf7Y+bQM7v5sDUt3n+C1PvW0iHiLdo9D+nlY9rbdSZSHuqd1JZ7tXotftx1n1H/XkpqRaXekPNNC4mp/zIXDcdB2LATlbOqS5NQMhny6hlX7TvLmrfXpF3vFUc3K00RUh3q3weqP4Nwxu9MoDzWkZUVevKUO83YkMPyLtaSke3cx0ULiSllZsOBFKFoBGgzM0UfOOZbGXXvgNG/3b0ivhtGuzaicr+2jkJUBS96wO4nyYIOalefVPnVZvCuRez6P40Ka9xYTLSSutH22dSd7u8ch8NpzYCVdSGfw5NVsPHSG9wY0pEf90m4IqZyuWCVoOAjiPoUz/jPfksq92xqX4/W+9Vm25wR3f7bGa9eB10LiKllZsPBlKFHNmtzvGpIupHPH5FVsPZLEhIGN6Fo36pqfUR6szVjrrvfF4+xOojxc35ho3r6tAav2nWTIp2v4M9X7iokWElfZNhMSd0Dbf19zCd2k8+kMnryKbUfP8sHAGDrXLuWejMp1CkdDozthw1faKlHX1LNBGd7u35C4/ae4ywuLiRYSV8jKstYbKVHdGg56FUnn0xk0eRU7jp5j4qAYOtW6vokclQdq9TBIgPaVqBzpUb807/RvyNqDp72umGghcYW/WiOPXrU1crGI7Dx2jomDG9GxphYRn1K4DDS6A9b/V1slKke61y/NO/0bsPbgaYZ8uppkLykmWkicLSsLFr1m9Y1cpTVy5nwaAyevZOexc3w4OIYONbSI+KS/WiVv2p1EeYmb65VmfP+GrDt4hiGfeEcx0ULibNtnQeL2q/aNnDmfxqDJq/jjWDIfDo6hfY1IN4dUblM4WlslKte61YtifP+GrD/kHcVEC4kzZWXBwlev2hr5WxG5Q4uIX2j1sDWCS1slKhe61Yvi3QHeUUy0kDjT9tlXbY1Yo7NW/6+IVNci4hcKR0PDwY5WyaFrb6+Uw011/1dM7vp0tcd2wGshcZa/Rmpl3xpJupDOHZ+s+qtPRIuIn2k9xvpzqbZKVO7cVDfqrz6Tuzz0pkUtJM6yfTYkbIM2l4/UOpuSzh2frLbuExnUSC9n+aOLfSXrvtRWicq1bvWiePu2BsTtP+WRd8DnupCISKhjsalaImLTmrUe5uJIreJVoU7vv711LiWdOyavZtuRJCYMjNEhvv6s1cPWn0vfsjeH8krd65fmrdsasHrfKYZ+5llzc+WokIhIuIiMEpHFQBKwG9gCHBORgyLykYg0dmVQj7bjB0jYelnfyMUJGLccTuK92xtxg95s6N+KlIVGg2HdF5AUb3ca5YV6NijDm7da06kM/XyNxxSTaxYSERkD7AfuBn4DegINgGpAc+BZrAWyfhORX0SkqouyeqYrtEYuTgW/Kd4qIjfqtCcKoJWjr0RHcKnrdEvDMozrV58Ve08y7Is4j5iCPictkmZAW2NMY2PMC8aYucaYzcaY3caY1caYT4wxdwElsdZUb+vSxJ5m5xw4vsWapM/RGjmflsHdn65hw6EzvDugIV3qaBFRDkXKQsOBsP5LOHvE7jTKS/VuFP3XrMEjvrR/PZNrFhJjzK3GmC0AV+sTMcakGmMmGGM+dmZAj2aMNVKrWCWo0wewlse9+7M1xB04xdu3NdBZfNXlWo0BkwXL3rE7ifJifWOiebV3PRb9kci9X62zdaXF3Ha2LxeRSi5J4o3+mAvHNkHrRyAwiJT0TO75Yg2r953irdsa0F3XE1HZKVoe6veHtZ/BueN2p1Fe7NbGZflPr7rM35HAfV+tJy0jy5YcuS0kc7CKSaNLXxSRNiKyzHmxvIAxsPg1KFIO6t1KSnomw76IY/mek7zetz49G5SxO6HyZK3GQGYaLB9vdxLl5W5vWo4Xetbm9+3HeWDKOtIz3V9MclVIjDEPAuOA+SLSWUQaiMgvwALAvyYS2jMPDq+F1v8i1QQw8r9rWbLrBK/2qUefGF0eV11D8cpQ91aI+wSSE+1Oo7zc4OYVeKZ7LeZuPc5D32wgw83FJNf3kRhjxgEvAz8Ca4BzQD1jzAAnZ/NcxlgjtQpFk1anP/d9tY6FOxN5uXddbo0ta3c65S3aPALpF2DFe3YnUT7grpYVeapbTX7afJSHp210azHJVSERkbIi8iHwPFYRSQV+MsZsdUU4j7VvMRxaRWbLB3lg2hZ+357AC7fUYUCTcnYnU96khGPI+JqP4fwpu9MoH3BP60o81rUGP2w8wtjpm8jMMm45bm5bJLuAhsDNxpiWQA/gbRF50unJPNmi1zDhUYz5ox5ztx7n2e61GNysvN2plDdqMxbSkmHlBLuTKB8xsm1lHulcjRnrD/Pv7zaR5YZikttCMtAY08QY8xuAMWY+1n0j94qIf/xP2L8MDixlRr4+zNp6kqe61WRIy4p2p1LeKrIm1OoJqz6EC6ftTqN8xP0dqvJgx6pMXxvPkzM3u7yY5Laz/btsXtsItADaOSnTX0Ski4jsFJHdIvJYNu+HishUx/urRKSCszP8k1n0GmcDi/HEwRge7VKde1rraGiVR23GQupZq5go5SQPdarKve0qM2X1IZ6evQVjXFdMnDL7rzHmANDSGfu6SEQCgfeBrkAtYICI1PrHZkOB08aYKsBbwKvOzPBPWQdWIvsWMj6lK/feUJd721Vx5eGUvyhVF6p3sy5vpZy1O43yESLC2BurM7xNJf678iDP/7jNZcUkJ3Nt5ei6jTHmtFicNWypCbDbGLPXGJMGfIM1z9elegKfO55PBzqKiDjp+H9jjGHX9Kc5acIp1Go4ozv615RiysXajoWUJFitrRLlPCLC411rcFfLChxZ8S1LPh6LSU9x+nFy0iJZISKTRaT5lTYQkaIiMgrYxuU/7K9XGeDShRviHa9lu40xJgNrZuLiV8g4XETiRCQuMTH34/aTzpykQPJBNpcbzANd6uf680pdVemGULUzrJgAqcl2p1E+RER4ulsNXig0g3JH53I+0/nLUAXlYJsawJPATyKSBawFjgApQFGsy041gdXAQ8aYuU5P6QTGmEnAJIDY2Nhct++KFC1BwNj1tA22vjFKOV2bR2FyJ4ibDC0ftDuN8iGyfTaRKfu50GMS+cJCnL7/nEzaeMYYMxbrt/+RwHagCFARyMC6tNTQGNPSyUXkMHDpZbJox2vZbiMiQUBh4KQTM/xNofz5kOB8rtq98ndlG0PlDrBsPKSdtzuN8hVZWbB4HBSvSr4GfV1yiJy0SAAwxlzA6oeY7pIkl1sDVHX00RwG+gO3/2Ob2cCdwAqgLzDfuHJoglKu1uZR+LQLrP0Umt9ndxrlCy4uddFr0mXLgDtLni6WOZbbfdyxemIbESnqrGCOPo/7gblYraBpxpitIvK8iPRwbDYZKC4iu4ExwGVDhJXyKuWbQ4XW1hTz6RfsTqO83cWlLopW/GupC1fIa6/LbOA8UABrKO48EdmT51QOxpg5xphqxpjKxpiXHK89bYyZ7XieYozpZ4yp4rhRcq+zjq2Ubdr+G5KPw7ov7U6ivN2uX62lLtpYS124Sl73fMwY87fVeRz3fyilrleFVlCuBSx9C2LuhKBQuxMpb3SxNVKkHNS7zaWHymuLZJ6I3HXpC8YY+xcQVsqbiVj3lZw7Ahu+sjuN8lZ75ltLXbQaA4HBLj1UXgtJLPCsiOwTkWki8qSIdHdGMKX8WqX2EN0YlrwJGWl2p1He5mJrpFA0NPjnGCXny+008rc7OtgDAIwx3Ywx5YF6WFOUJAAdnR9TKT8jYvWVJB2CTd/YnUZ5G8dSF7R6yC2XRnPbR/IGEAmkiMhWYD3wGzDDGLMCaxiuUsoZqnSy7nhf8gbUv92lnaXKxyx+HQqWgoaD3XK43M7+G4V1Y2JvrPtJCgMfAatFpIjT0ynlz0Ss+0pO74fN39qdRnmL/ctg/xKrNRIc5pZD5vbSVjVjzDFjzFxjzGvGmP5AeeAU8KwrAirl16p3tWYHXvw6ZGbYnUZ5g8WvQYEIaHSn2w6Z2872HSJyTkSWi8gHIjICay6up4BBzo+nlJ+72Fdyag9suWw5IKX+7sAK2LsQWj4EIfnddtjcXnQtDTTA6lxvAIwGqgECiIjMwJq8cYMx5mfnxVTKj1XvBiXrWL9p1u3rsmkulA9Y9IrVGom9262HzW0fyTFjzC+Oy1q3G2NqA+HAzVjF5BTQDZji/KhK+amAAKtVcnK3tkrUlR1c6WiNPOjW1gjkskUiIueATcAGx2MT8CdwG7DLGDPUyfmUUgA1brZaJYteteZM0laJ+qeF9rRGIPd9JAOAOUAEMBZYjlVM+mFd5lJKuUJAALR9VFslKnsHV8LeBdBiNIQUcPvhc9UiMcb8CPx48WsRyQ9EAUeNMbqAglKuVKM7RNaGRa9pq0T93cJXIH8JaGzPRaE8TZFijDlvjNmjRUQpNwgIgHb/hpO7YMv3dqdRnuLgKqs10vJBW1ojkPe5tpRS7lSjO0TWsvpKsnR+VIU1UsvG1ghoIVHKu/w1gktbJQqrNbJnPrS0p2/kIi0kSnmbmj20VaIsi16B/MWh8T22xtBCopS3+WsE1y7YOsPuNMouh1ZbrRGbRmpdSguJUt6oZk+IqGmN1tFWiX9a+LJHtEZAC4lS3ikgANo9ZrVKdGZg/3NguaNv5EEILWh3Gi0kSnmtmj2smYEXvgyZ6XanUe5iDMx/EQpEQuNhdqcBtJAo5b0CAqD9U9Z6Jbq2u//YuxAOLIM2j7h9Tq0r0UKilDerdiOUiYVFr0NGqt1plKtdbI0UioaYIXan+YsWEqW8mQh0eArOxsPaz+1Oo1ztj7lwOA7ajnXLWuw5pYVEKW9XqR2UbwVLxkGazlbks7KyYMGLULQCNBhod5q/0UKilLcTgQ5PQvJxWPOx3WmUq2yfDcc2Q7vHITDY7jR/45GFRESKichvIrLL8WfRK2yXKSIbHI/Z7s6plMco3wIqd4Slb0HqObvTKGfLyrRG55WoBnX72Z3mMh5ZSIDHgHnGmKrAPMfX2blgjGngePRwXzylPFCHJ+HCKVg50e4kytm2fAeJO6D9Ex65fICnFpKewMWew8+BW+yLopSXKBMD1W+C5e/ChdN2p1HOkplutUZK1rFmNPBAnlpIShpjjjqeHwNKXmG7MBGJE5GVInLL1XYoIsMd28YlJiY6M6tSnqP9E5CaBCvetzuJcpaNU+DUXmj/pHXvkAfK1QqJziQivwOlsnnryUu/MMYYETFX2E15Y8xhEakEzBeRzcaYPdltaIyZBEwCiI2NvdL+lPJupepC7V6wYgI0GQ4FI+1OpPIiPQUWvgqlG0H1rnanuSLbypsxppMxpk42j1nAcRGJAnD8mXCFfRx2/LkXWAg0dFN8pTxX+6cgI8Vakld5t9WTrHuEOj1rjc7zUJ7ZToLZwJ2O53cCs/65gYgUFZFQx/MSQEtgm9sSKuWpSlSBmDth7adwMtsGuvIGF07Dkjes0XiV2tqd5qo8tZC8AtwgIruATo6vEZFYEbk4UL4mECciG4EFwCvGGC0kSgG0fQwCQ2D+C3YnUddr6VuQkgQ3PGd3kmuyrY/kaowxJ4GO2bweB9zjeL4cqOvmaEp5h/CS0Px+WPwatHjAGtGlvEdSvDWMu95tVr+Xh/PUFolSKq9aPAD5S8Bvz1iT/SnvseBlwFij8LyAFhKlfFVYIWtJ3v1LYPfvdqdROXV8G2z82hp1V7S83WlyRAuJUr4s5i4oWtFqleiSvN5h3nMQEg6t/2V3khzTQqKULwsKgY7/BwlbYdM0u9Ooa9m/DP74BVo9BPmL2Z0mx7SQKOXravWCqAaw4CXrBjflmYyB356G8NLQbJTdaXJFC4lSvi4gAG54HpIOwZqP7E6jrmT7bGvRqvaPQ3A+u9PkihYSpfxBpbbWjW2Lx8H5U3anUf+UkQa/PwcRNaD+7XanyTUtJEr5ixueh9SzsPAVu5Oof1o9CU7tsb5HgR55e99VaSFRyl+UqmON4lrzsTXEVHmG5ARY9CpUuQGq3Wh3muuihUQpf9LhKQgNh18e05sUPcX8FyD9PHR52e4k100LiVL+JH8xa12LfYtgx092p1FH1sO6L6HpSChR1e40100LiVL+JvZuiKgJc5/Q4cB2MgZ+fgzyF7dmIPBiWkiU8jeBQdD1FThzAFbqSoq22fIdHFoJHZ+GsMJ2p8kTLSRK+aNK7aDGzbD4DTh7xO40/iftT/j1/yCqPjQcZHeaPNNCopS/6vwiZGVY9y8o91r6Npw7Al1ehYBAu9PkmRYSpfxVsYrQ4n7Y9A0cWmN3Gv9x+gAsHw91+kL55nancQotJEr5s1ZjIDwKfn4UsrLsTuMffvs/QLxi5cOc0kKilD8LLQidnoMj66w13pVr7foNts2C1mOgcLTdaZxGC4lS/q7erVCxLfz+rHa8u1JqMvw4BkpUg5YP2p3GqbSQKOXvRODmtyAzDeaMtTuN71r4MiQdhO7jISjU7jROpYVEKQXFK0O7x2DHj7D9B7vT+J7D62DlBGuuMx/pYL+UFhKllKX5/VCyrtUqSUmyO43vyEyHH0ZDgUif6mC/lBYSpZQlMBh6vAPJx/XeEmdaOQGObYabXvf6O9ivRAuJUup/ysRYEwjGTYaDK+1O4/1O7YMFL0P1blCzu91pXEYLiVLq79o/CYXLwuzRkJFqdxrvZQz8+BAEBEG3cdagBh+lhUQp9XehBaHbm3BiJyx9y+403mvjN7B3IXR6BgqVtjuNS3lkIRGRfiKyVUSyRCT2Ktt1EZGdIrJbRB5zZ0alfFq1zlCnDyx5Q1dTvB7JCdY0/WWbQuxQu9O4nEcWEmAL0BtYfKUNRCQQeB/oCtQCBohILffEU8oPdHkVQgvBd/fouiW5kZUFM0dZqx72eBcCPPXHrPN45BkaY7YbY3ZeY7MmwG5jzF5jTBrwDdDT9emU8hMFI+CWDyBhq3XXu8qZ1R/C7t+t2ZUjqtudxi08spDkUBng0CVfxztey5aIDBeROBGJS0xMdHk4pXxCtc7QZASs+sCaJ0pd3bEt8NvTUK0rNL7H7jRuY1shEZHfRWRLNg+XtCqMMZOMMbHGmNiIiAhXHEIp33TD8xBZy7pck5xgdxrPlX4BvhsK+YpCz/d8epTWPwXZdWBjTKc87uIwUPaSr6MdrymlnCk4DPpMhkntYNZ9cPs0v/ohmWO/PgWJO2DwDChQwu40buXNl7bWAFVFpKKIhAD9gdk2Z1LKN5WsZV3z3/UrrJ5kdxrPs/NnWPOxNc1M5Q52p3E7jywkItJLROKB5sBPIjLX8XppEZkDYIzJAO4H5gLbgWnGmK12ZVbK5zUZBlVvtNYaP67/1f5y7pjVUitVFzo+bXcaW4gxxu4MbhcbG2vi4uLsjqGU90lOhA9aQP7iMHwBBOezO5G9srLgqz5wYAWMWOTTo7REZK0xJtv7+jyyRaKU8lAFI6DXB5C4HX540JoGxJ8tfBn2zIcu//HpInItWkiUUrlTpRO0fwo2TYWlb9qdxj6bp8Pi16DhIGudET9m26gtpZQXa/OINUJp3vPW0rE+PLNttuLjYOa9UL4ldHvL70exaYtEKZV7Ita9EmVi4PvhcHST3YncJykevrkdwkvBrV9CUIjdiWynhUQpdX2C80H/r60b8KYMgHPH7U7keml/Wueadh5unwoFitudyCNoIVFKXb/wUjBgClw4BVMH+vbkjllZMGMkHN8CfT+ByJp2J/IYWkiUUnkTVR96fQjxa2D2A747kmvhf2D7bLjhBWsOMvUXLSRKqbyr1QM6PAWbp1kzBftaMVkzGRa/Dg0HQ/P77E7jcXTUllLKOVo/AmePwLK3wWRav7n7wmimVZPg57FQrYu1cqQvnJOTaSFRSjmHiPWDNiAIlr8LmRnQ5WXv/sG7YgLMfRyqd4N+n+kIrSvQQqKUch4R6PoaSKC1hklWBtz0uncWk2Xj4bf/g5o9rM71wGC7E3ksLSRKKecSsVoigY6WSVaGo6XiRV2yS96wbras3Qt6f6RF5Bq0kCilnE/E6iMJCIKlb1nFpPt47ygmi16DBS9B3X5wy0SrIKqr0r8hpZRriEDHZ6xisvh1OH8KbnnfuoHRE6WnwC+PwdpPoV5/uGUCBATancoreMGvB0opryViDQvu8grsmgsT20D8WrtTXe7kHvi4k1VEWj6oRSSXtJAopVyv2Si4ey5g4JMbrdFQnnKvyZbv4MM2cDbeWkb4hue1iOSSFhKllHtEx8KIxVD1BmtI7dRBcOG0fXnSU+DHMTD9boisBSOXQrUb7cvjxbSQKKXcJ38xa6LHG/8Df/xitQT2LXF/jmObYfINEDcZWoyGu+ZA4Wj35/ARWkiUUu4lYk0zcvdcMMDnN8PnPeDgStcf+/g2mDoYJraCpEMwYCp0fkGH9+aRjtpSStkjOhbuXw1xn1hDhD+5ESp3hPZPWO85U+JOWPgKbJ0BIQWh7b+h2b2Qr4hzj+OnxHhKh5cbxcbGmri4OLtjKKUuSvsT1nwMS9+2pqSveiM0HQ7lmkNIgevbZ0aqtZLh2s9g87cQnB+ajYTm91uX2FSuiMhaY0y2FV5bJEop+4UUsIbdxt4NqydZ05PsmgsBwVbrpGIbqNAaohtDcFj2+8jMgKMbYN8iq9/l4ErIuGAVkJajrb6QAiXcelr+QlskSinPk3YeDi6HfYutonB0A5gsCAqDIuWzn7sr6TCknbOeR9b6X/Gp0EovYTmBtkiUUt4lJD9U6WQ9AC6cgYMrrMJy9nD2nynf0ioaFVpDwQi3RVVaSJRS3iBfEaje1Xooj6PDf5VSSuWJRxYSEeknIltFJEtErjgOUET2i8hmEdkgItrpoZRSNvDUS1tbgN7AhznYtr0x5oSL8yillLoCjywkxpjtAOKNq6oppZSf8chLW7lggF9FZK2IDL/ahiIyXETiRCQuMTHRTfGUUsr32dYiEZHfgVLZvPWkMWZWDnfTyhhzWEQigd9EZIcxZnF2GxpjJgGTwLqP5LpCK6WUuoxthcQY08kJ+zjs+DNBRGYATYBsC4lSSinX8NpLWyJSQETCLz4HOmN10iullHIjj5wiRUR6Ae8CEcAZYIMx5kYRKQ18bIy5SUQqATMcHwkCvjbGvJTD/ScCB64zXgnA30aJ6Tn7Pn87X9Bzzq3yxphspwzwyELiyUQk7krzzfgqPWff52/nC3rOzuS1l7aUUkp5Bi0kSiml8kQLSe5NsjuADfScfZ+/nS/oOTuN9pEopZTKE22RKKWUyhMtJEoppfJEC8kViEgXEdkpIrtF5LFs3g8VkamO91eJSAUbYjpNDs53jIhsE5FNIjJPRMrbkdOZrnXOl2zXR0TM1ZY08BY5OWcRudXxvd4qIl+7O6Oz5eDfdjkRWSAi6x3/vm+yI6eziMgnIpIgItneoC2W8Y6/j00i0ijPBzXG6OMfDyAQ2ANUAkKAjUCtf2xzLzDR8bw/MNXu3C4+3/ZAfsfzUd58vjk9Z8d24VjT7qwEYu3O7Ybvc1VgPVDU8XWk3bndcM6TgFGO57WA/XbnzuM5twEaAVuu8P5NwM+AAM2AVXk9prZIstcE2G2M2WuMSQO+AXr+Y5uewOeO59OBjuK9895f83yNMQuMMecdX64Eot2c0dly8j0GeAF4FUhxZzgXyck5DwPeN8acBmseOzdndLacnLMBCjmeFwaOuDGf0xlr4tpTV9mkJ/CFsawEiohIVF6OqYUke2WAQ5d8He94LdttjDEZQBJQ3C3pnC8n53upoVi/0Xiza56zo8lf1hjzkzuDuVBOvs/VgGoiskxEVopIF7elc42cnPOzwCARiQfmAA+4J5ptcvv//Zo8cmEr5blEZBAQC7S1O4sriUgA8CYwxOYo7haEdXmrHVarc7GI1DXGnLEzlIsNAD4zxrwhIs2BL0WkjjEmy+5g3kJbJNk7DJS95Otox2vZbiMiQVhN4pNuSed8OTlfRKQT8CTQwxiT6qZsrnKtcw4H6gALRWQ/1rXk2V7e4Z6T73M8MNsYk26M2Qf8gVVYvFVOznkoMA3AGLMCCMOa3NBX5ej/e25oIcneGqCqiFQUkRCszvTZ/9hmNnCn43lfYL5x9GR5oWuer4g0BD7EKiLeft0crnHOxpgkY0wJY0wFY0wFrH6hHsaYOHviOkVO/l3PxGqNICIlsC517XVjRmfLyTkfBDoCiEhNrELiy8uozgbucIzeagYkGWOO5mWHemkrG8aYDBG5H5iLNerjE2PMVhF5HogzxswGJmM1gXdjdWz1ty9x3uTwfF8HCgLfOsYUHDTG9LAtdB7l8Jx9Sg7PeS7QWUS2AZnAWGOMt7a0c3rO/wI+EpGHsTreh3jxL4WIyBSsXwZKOPp9ngGCAYwxE7H6gW4CdgPngbvyfEwv/vtSSinlAfTSllJKqTzRQqKUUipPtJAopZTKEy0kSiml8kQLiVJKqTzRQqKUUipPtJAopZTKEy0kSiml8kQLiVI2E5G+IpJ66WJhIvKOiOwRkZJ2ZlMqJ/TOdqVs5ljHZg2w3hgzTEQeAR4FWhpjdtmbTqlr07m2lLKZMcaIyBPATyKyB3gC6KhFRHkLbZEo5SFEZDnWin7djTHevnCY8iPaR6KUBxCRDkB9rHW0j9scR6lc0RaJUjYTkfrAYuBhoBtQ0Bhzo72plMo5LSRK2cgxUmsFMNEY87yI1AE2AR2MMQttDadUDmkhUcomIlIMWAYsNsaMuOT1qUA5Y0xz28IplQtaSJRSSuWJdrYrpZTKEy0kSiml8kQLiVJKqTzRQqKUUipPtJAopZTKEy0kSiml8kQLiVJKqTzRQqKUUipP/h+5SQLIDwf7MQAAAABJRU5ErkJggg==\n",
20 | "text/plain": [
21 | ""
22 | ]
23 | },
24 | "metadata": {
25 | "needs_background": "light"
26 | },
27 | "output_type": "display_data"
28 | }
29 | ],
30 | "source": [
31 | "import numpy as np\n",
32 | "import matplotlib.pyplot as plt\n",
33 | "\n",
34 | "def psi(n,L,x):\n",
35 | " psi=np.sqrt(2.0/L)*np.sin(n*np.pi*x/L)\n",
36 | " return psi\n",
37 | " \n",
38 | "L=1.0\n",
39 | "\n",
40 | "x=np.linspace(0.0, L, 51)\n",
41 | "\n",
42 | "f1=np.zeros(51)\n",
43 | "f2=np.zeros(51)\n",
44 | "\n",
45 | "for i in range(51):\n",
46 | " f1[i]=psi(1,L,x[i])\n",
47 | " f2[i]=psi(2,L,x[i])\n",
48 | "\n",
49 | "plt.plot(x,f1)\n",
50 | "plt.plot(x,f2)\n",
51 | "plt.legend(['n = 1','n = 2'])\n",
52 | "\n",
53 | "plt.xlabel(\"$x$\", fontsize=14)\n",
54 | "plt.ylabel(\"$\\psi_n(x)$\", fontsize=14)\n",
55 | "plt.savefig('PIB.png') \n",
56 | "plt.show()"
57 | ]
58 | },
59 | {
60 | "cell_type": "markdown",
61 | "id": "52532267",
62 | "metadata": {},
63 | "source": [
64 | "# Non-stationary state"
65 | ]
66 | },
67 | {
68 | "cell_type": "code",
69 | "execution_count": 2,
70 | "id": "b05be02c",
71 | "metadata": {},
72 | "outputs": [
73 | {
74 | "data": {
75 | "image/png": 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wLrih0w0EuAbw3oH39A6lQaxV4c7S9GxRVAOPSSm7AAOAB4QQtVXY2CKljKu5vWzdEFuWRftS8XN3YlQnC9cGsJIuYdqA/IJdKWpQu56WnlhKcmEyD/V6CGcHZ73DucDN0Y27ut3F7ozd7D63W+9w6k0liiaSUp6TUu6r+boISATC9YqnpSsorWJtQibT4sJxdmw+PZI39o/iZHYJvyWrQe2rKasu44MDHxAXFMfIyJF6h3OZ2R1nE+wWzLsH3rWbxH9xhbumbAp48uRJgoKCiI6OJi4uDn9/f9q1a0dhYaEZo70ym9jpTQgRDfQEdtXy8EAhxEEgHXhcSplQy/n3APcAREVFWTDS5mvZoXQqjSa7nu1Um8ndQ/n78iMs2JVCvzb+eodj0xYkLiCrLIv/G/5/NlegCsDFwYW7u9/Nq7teZXv6dgaHD673uf/c/U+Onj9q1ng6+XfiqX5P1XmMNSrcWYPuiUII4QksBh6WUv4xPe4DWkspi4UQE4GlQIc/XkNK+THwMUCfPn3s46OGjVm8N5VOIV50DbPOL561uDs7MqNXON/9dpYXSirx87Cd7hRbUlBRwLz4eQwNH0rvVr31DueKru1wLZ/Ff8Z7B95jUNggm0xoDWGOCnfWoGuiEEI4oSWJb6SUS/74+MWJQ0q5UgjxvhAiUEqZY804m7sTWcUcOJvPsxM72/0fXm3m9Iti/o4UFu9L5a6h9rV3lbV8Fv8ZxZXFPNTrsjklNsXZwZk/df8TL+54kc2pmxkeObxe513tk79emlrhzlp0SxRCe0eaByRKKd+6wjEhQKaUUgoh+qGNqeRaMcwWYfG+VBwMgmk97XvtxJV0DvWmZ5Qv3+4+w51D2jTLZNgUmSWZfJP4DZPaTqKjv/U+pTbW1PZT+fTwp7x34D2GRQyz6Z+npSvcWYueo5aDgVuAURdNf50ohLhXCHFvzTGzgPiaMYp3gBukvYxi2QmjSbJkXyrDY4II9nLVOxyLmdNPG9Teffq83qHYnA8OfoBRGm1qOmxdnAxO3Bd3H4nnE1l/Zr3e4dTJ0hXurEW3FoWUcitQ50cBKeW7wLvWiahl2noih8zCCl6Y0rwGsf9oSvcw/r7iCN/uPkP/tgF6h2MzThecZumJpVzf8XoivOznd2Bim4l8cugT3jvwHqOiRtl0jW1LVrizFtv931WsYvHeVHzcnBjduXmsnbgSN2cHZvQMZ2V8BnklaqX27/67/7+4OLhwT/d79A6lQRwNjtzX4z5O5J9gdfJqvcNp9lSiaMEKy6tYnZDB1B5huDg66B2Oxd3Y//eV2ql6h2ITDmcfZm3KWuZ2nUuAm/21ssa3GU+0dzRfHflK71CaPZUoWrCVh85RUd381k5cSacQb3rVDGqroS54/+D7+Ln4MbfrXL1DaRSDMHBDpxs4nHOYhNzLllcBqJ9zLRrzf6ISRQv28+FzRAe40z3CR+9QrOa6PpGczC7hUGqB3qHoKikvia1pW7mp8014ONlXFcOLTW03FTdHN74/9v1lj7m6upKbm6uSxUWklOTm5uLq2rCJK7ovuFP0kVdSyfaTudw9tK1NTy80twndQnl+WQI/7k+jh50WZjKHLxO+xM3Rjes7Xq93KE3i5ezFpLaTWHFyBY/2fhQfl/996ImIiCA1NZXs7GwdI7Q9rq6uREQ0rBdBJYoWam1iJkaTZGK3EL1DsSofNyfGdA5m+cF0np3UGSeHlteozizJ5OfTPzM7Zja+rr56h9Nk13e8nkXHF7Hs5DJu6XLLhfudnJxo06aNjpE1Hy3vr0QB4Jf4DMJ93egW3nK6nX43PS6c3JJKtia1zAX+C44uwCRNl7yp2rNO/p3oEdSDhccWqtraFqISRQtUWF7FlqRsJsSGtKhup9+N6BiMr7sTP+5veXUqSqpK+OHYD4yJGkOkV6Te4ZjN9R2vJ6UwhV3nattXVGkqlShaoA2JWVQZJRNaWLfT75wdDUzuHsqaIxkUV1TrHY5VLT6+mKKqIm6PvV3vUMxqXPQ4/Fz8ah3UVppOJYoWaFX8OVp5u9Az0k/vUHQzo2c45VUmfonP0DsUq6kyVfF14tf0btWb2MBYvcMxKxcHF2Z0mMHGsxvJKGk5P1NrUYmihSmpqObXY9mM7xqCwdDyup1+1yvKjyh/d5a2oO6nNclrOFdyjtu7Nq/WxO9mx8zGJE0sTlqsdyjNjkoULcyvx7KpqDYxoVuo3qHoSgjB9J7hbDuZQ2Zhud7hWJyUki8TvqSNTxuGRgzVOxyLiPCKYEj4EBYfX0yVqUrvcJoVlShamJXx5wj0dKZvtKr2Nj0uDClh2YF0vUOxuF0Zu0g8n8htXW+z6Q30muqGTjeQXZbNxjMb9Q6lWWm+vzHKZcqrjGw8msW4riE4tOBup9+1DfKkR6QvS1pA99MXCV8Q4BrApLaT9A7FogaHDSbcM5yFxxbqHUqzohJFC7LpeDallUYmxLbM2U61ubZnOInnCjmaYZ0i9Xo4nnecbWnbuKnzTbg4uOgdjkU5GByYHTOb3Rm7OZVv3a24mzOVKFqQX+Iz8HV3YoCqx3DB5O6hOBoES/c33+6n+QnzcXN047qO1+kdilXM6DADJ4MT3x9XU2XNRSWKFqKi2si6I5mM7dyqRW5bcSUBni4MjwnipwNpmEzNb/O4/PJ8Vp1exdR2Uy/ZB6k583f1Z1TUKFaeWqkGtc1EvWO0ENtP5FJUUc3EFj7bqTbTe4ZzrqCcnaebXzn2pSeWUmmqtPvN/xpqctvJ5FXksSN9h96hNAsqUbQQKw+fw8vFkUHtVbfTH43t0gpPF8dmt6bCJE0sPLaQ3q1608Gvg97hWNXgsMH4uviy4uQKvUNpFlSiaAGqjCbWJmYypkurFlHJrqFcnRyYEBvCysMZlFcZ9Q7HbLanbye1OJUbOt6gdyhW5+TgxDXR17Dh7AaKK4v1DsfuqUTRAuw8lUt+aRXj1WynK5oaF0Zxzar15mLh0YUEuAYwOmq03qHoYnLbyVQYK1h/Zr3eodg9lShagNUJGbg7OzA8JkjvUGzWwLYBBHg4s+JQ85j9lF6czqbUTVzb4VqcHJz0DkcXPYJ6EOEZwYpTqvupqVSiaOaklKxPzGJoh0BcnVS305U4OhgYHxvC+sQsSivtf0fZRccXIYRgdsxsvUPRjRCCye0ms+vcLrJKs/QOx67pliiEEJFCiI1CiCNCiAQhxEO1HCOEEO8IIU4IIQ4JIXrpEas9S0gv5FxBOaM7t9I7FJs3pUcYZVVG1ifa95tKpbGSxUmLGR4xnFBPnWe56VyvelKbSUgkq06v0jUOe6dnKdRq4DEp5T4hhBewVwixVkp55KJjJgAdam79gQ9q/lXqaX1iFkLAqE7Beodi8/pG+xPs5cKKQ+lM6RGmdziNti5lHefLz+s3iF14Do6ugMRlkLIDnD3AIwg8ArWbeyB4hUL368DfsqVKo32i6RbYjRWnVjC361yLPldzpluikFKeA87VfF0khEgEwoGLE8U0YL6UUgI7hRC+QojQmnOVelh/NJO4SF8CPZv31g3m4GAQTOwWyoLdZygqr8LL1T779hceW0iUVxQDwgZY70nzkiFxORxZBqm7tfsCY6Df3WCsgpJsKM2FnCQo2aF9vfn/oOfNMOwJ8ImwWGiT2k7i9d2vk5SX1OKmCZuLni2KC4QQ0UBP4I91DMOBsxd9n1pz3yWJQghxD3APQFRUlMXitDeZheUcSi3giWs66h2K3ZjSI4wvtiezLjGTGT0t9+ZlKcfOH2Nf1j4e7/O4dXaJrSiC1X+FffO170O6w6i/QeepEFTH713hOdjyJuz9Ag4sgN63wdDHwMv8M/PGR4/njd/e4OdTP/Nw74fNfv2WQPfBbCGEJ7AYeFhK2aid2aSUH0sp+0gp+wQFqZk9v9twVOtrH91ZdTvVV68oX8J93Vh+0D4brd8f+x4XBxemtZtm+SdL3gofDIL9X8OgP8NDB+HeLVoLoa4kAeAdCpP+BX/ZDz3mwG/z4D89YPWzUG7eDRoD3AIYFDaIn0//jEmazHrtlkLXRCGEcEJLEt9IKZfUckgacHEF+Iia+5R6WJ+YSbivGx1beekdit0QQjCpeyhbkrIpKLWvfYKKK4tZfmo546PH4+vqa7knqirX3tC/mAzCAW7/Bca9An7RDb+WbyRMfQf+vAe6zoCd78OXk6Ekx6whT247mYySDPZm7jXrdVsKPWc9CWAekCilfOsKhy0Dbq2Z/TQAKFDjE/VTXmVk64kcxnQORvuvVuprcvdQqoyS1Qn2VXt5xakVlFWXcUMnCw5ip++Hj4fDjneh751w3zaIMsP8Ev+2MONDmLMQso/B5xOg0HxrWkZGjcTd0Z2fT/1stmu2JHq2KAYDtwCjhBAHam4ThRD3CiHurTlmJXAKOAF8AtyvU6x2Z9uJHMqrTGpabCN0C/ehdYA7y+1o8Z2UkoXHFtIloAuxgbGWeZI9n8OnY6C8AG5eDJPe1GY0mVPMOLh5iTaG8dk1kHvSLJd1c3RjTOsxrEleQ4WxwizXbEl0SxRSyq1SSiGl7C6ljKu5rZRSfiil/LDmGCmlfEBK2U5K2U1KuUeveO3NusQsPJwd6N9WlTxtKCEEk7uHsv1kLrnF9vGmcjD7ICfyT1hugd3uT2DFw9B2JNy/A9qPsczzAEQPhrnLoKJYa1lkHrn6OfUwue1kiqqK2Jy62SzXa0l0H8xWzE9KyYajmQyLCVKbADbS5O5hGE2SVfH20f20OGkxbo5uTGgzwfwX3/URrHwcYibADd+Am5/5n+OPwnvB7atAGLRkkdr0sYV+If0IcgtSO8o2gkoUzVB8WiGZhRWq26kJOoV40S7Iwy72fiquLGZ18momtpmIh5OZu4J2vA+rnoROk+G6+eBoxfU4wZ3gjl/AzRfmT4Uzf5w93zAOBgeuib6GrWlb1Y6yDaQSRTO0LjETIWBkRzVVuLGEEEzpEcau0+fJKizXO5w6rTy9krLqMmbFzDLvhbf/F1Y/o62JmP0FODqb9/r14RcNd6wGz2D4YW6TZ0ONix5HpalSdT81kEoUzdD6o5n0ivIjQK3GbpLJ3cOQEn4+bNsT7RYdX0RHv450DehqvotufRvW/A26TIdZn4GeO9B6hWitmdLzsOQeMDV+LUSPoB4EuwWzJmWNGQNs/lSiaGYyCsqJTytUi+zMoH2wJ51CvFhxyHYTRUJuAonnE5kZM9N806B3fgDrXoDYmTBznr5J4nch3WD8a3ByPWz/T6MvYxAGxrQew9a0rZRWlZoxwOatwYlCCOEihGgjhOgihFB9GzZm/dFMAMao8QmzmNIjjL0peaTll+kdSq0WH1+Mq4Mrk9pOMs8Fk9ZqW3J0mgwzPgYHm9jlR9PnDq2Fs/7vcGZnoy8zLnocFcYK1f3UAPVKFEIILyHEfUKIzUAB2rqGeCBDCHFGCPGJEKKvJQNV6md9YhaR/m50CPbUO5RmYVI3bZvuVTbY/VRaVcrK0ysZFz0Ob2fvpl8w+zgsugOCu8K1NpYkAITQVnH7Rmpxlp5v1GXiguIIdAtU3U8NcNVEIYR4FEgG7gDWou3oGgfEAAOBF9E2F1wrhPhFCKG2Z9RJWaWRbSdyGN2plVqNbSbRgR7EhnvbZPfT6uTVlFSVMLPDzKZfrCwPvr0BHJxhzgLzL6QzF1cfbWC9JBuW3teoehcOBgfGRI1hS+oW1f1UT/VpUQwAhksp+0op/y6lXC2lPCylPCGl3C2l/ExKeTsQgrblxnCLRqxc0dYTOVRUm1S3k5lN6hbGgbP5nD1vW28qi5IW0danLT2DezbtQsZq+OF2yD8D138Nvja+A3NYT21vqeO/wI73GnWJcdHjKDeWsyVti5mDa56umiiklNdJKeMBhBDxQgifKxxXLqV8X0r5qbmDVOpnfWImXi6O9GujVmOb04Xup3jbaVUk5SVxKPsQMzuYYRB77XNwaiNMfgtaDzRPgJbW7x5tHGXdC5Da8A0begX3IsA1gDXJqvupPho6mN0FuGzOpRDCRwjRuNSumIWUko3HshgaE4izo5rMZk5RAe50j/DhZxvqflqctBgngxNT2k1p2oX2faXt2Nr/Puh1q3mCswYhYNq74BkCy/6itYoawMHgwJjWY9iStoWyatucqGBL6juYvUoI8RIguXTb79+5A38yZ2BKwxw5p63GHtlRTYu1hEndQjmYWmAT3U/l1eUsO7mMMVFj8HNtwnYaZ3bBike0/ZvGvWK+AK3FzU+bMpuVAHvmNfj0sa3HUlZdxta0rRYIrnmp70fPw2hjDwLYLYTIF0JsEkK8LYS4A3iEP1SdU6xrY02RohEqUVjExJruJ1tYfLc2ZS1FlUXMjGnCIHZJLvxwmzaDaPbntjfDqb46T4G2I2Djqw1etd27VW/8Xf1V91M91CtRSCmflFKOAKqAvsDNaDOgIoBngNnAkxaKUamHDUez6B7hQ5CXWo1tCZH+7vSI9LWJ7qfFSYuJ9Iqkb0gjZ6RLCT/dD6U52gwia2zyZylCwIT/g8oSWP9Sg051NDgyOmo0m1I3UV5t29u06K2hndmeUsp9UsoVUspXpJSzpJQdpJRtpJTfWiRC5arOl1Sy/2y+6naysMndQjmcVkBKboluMZwuOM3ezL1c2+HaxtfE3vWhNmNo3CsQ2sO8AeohqCP0v1cbb0nb16BTf+9+2pa2zULBNQ8N+k2TUtpXbcgWYvPxbKSEkZ1UorCkCd1CAH27n5YkLcFRODK9/fTGXSB9P6x5DjpO1GYONRfDnwKPIFj5RIP2guob0hc/Fz9Wp6y2YHD2T02PaQY2HssiwMOZ7uG1zlxWzCTCz52eUfp1P1UZq1h2chnDI4cT6BbY8AtUFGkrmj2DYdp7WrdNc+HqDWNfgrQ9cLD+nRuOBkdGRY1i01nV/VQXlSjsnNEk2XQ8m+EdgzAYmtEfvo2a1C2UhPRCTudYv/tpw9kNnC8/37iV2FLCikchLxlmfgruzXCtTfcbIKKvtraivKDep41rPY7S6lK2p2+3YHD2TSUKO7f/TB75pVWMUt1OVvH77KeVOnQ/LUlaQqhHKIPCBjX85IPfwuHvYcQz0LoR59sDgwEmvqHNfvr1n/U+rW9oX3xcfNTeT3UwW6IQQkQJ0djRNaWxNh7LwsEgGNpBbeRrDWG+bvRu7Wf1vZ/SitPYkb6DGe1n4GBoYHnbnCT4+TGIHgpDH7NMgLYirKe2cHD3R5B1tF6nOBmctNlPZzdRaay0cID2yZxv7MnAQSHEUDNeU7mKDUez6d3aDx83G6gZ0EJM6hZK4rlCTmZbr5zmkqQlCCGY0WFGw06sroRFt4OTG1z7CTQ0ydij0S9omxqufa7+p0SNpriqmF3nmlZutbkyZ6K4A1gC/MuM11TqcK6gjMRzharbycoudD9ZqVVRbapmadJSBocNJsQjpGEnb3wVMg7D1HfBO9QyAdoajwAY/DAkran3PlADQgfg4eTB+jPrLRubnWpQoqirUJGU8gsp5QtSyv5ND0upj1+PZQOo9RNWFuLjSt9oP6tNk92atpWssqyGr8RO3grb/gO9b4NOEy0Sm83qdw+4B8DGf9TrcGcHZ4aFD2Pj2Y0YTUYLB2d/Gtqi2C6EaGuOJxZCfCaEyBJCxF/h8RFCiAIhxIGa2/PmeN7mZMPRLMJ93YhppYoUWdukbqEczSjiRFaRxZ9r8fHFBLoFMixiWP1PKsuHH+8F/7ZwTf3eLJsVF08Y9BetdOrZ3fU6ZXTr0ZwvP8/+rP0WDs7+NDRRrERLFr0uvlMIMUwI0dCljV8A469yzBYpZVzN7eUGXr9Zq6jWihSN7BSkihTpYGK3UISA5Qct26rILMlkc9pmprefjpOhAeNQK5+AwnRtXMJWixBZWr+7wT2w3q2KoeFDcTY4q+6nWjR0ZfZDaGMQG4QQ44QQcUKIX4CNwJkGXmsz0Lhahgq7T5+ntNKoup10EuztyoA2ASw/lI5sRJW1+lp6YikmaeLa9tfW/6TDi7SpsMOfgojeFovN5jl7wOCHtFob9aix7e7kzqDwQaw/s96iP1N71ODBbCnlv4DXgBXAb0AR0F1KOcfMsQEMFEIcrNnmvOuVDhJC3COE2COE2JOdnW2BMGzPhqNZODsaGNSuESt0FbOY0iOMU9klHDlXaJHrm6SJH0/8SP/Q/kR617a7fy3yz2oL6yL6Nv+psPXR9y7wCK53q2J01GjOlZzjyPkjFg7MvjR0MDtSCPER8DJakqgAfpZSJlggtn1AayllD+C/wNIrHSil/FhK2UdK2ScoqGWsJ/j1WDYD2wbg5twCpjvaqPGxITgahMW6n3am7yStOK3+K7FNJq2OtKkarv3YfrcONydndxjyMJzeBMlX7x0fETECB+HA+hTV/XSxhrYokoCewGQp5WBgKvC2EOJZcwcmpSyUUhbXfL0ScBJCqI/PwOmcEk7nlKhpsTrz93BmcPtAlh+0TPfToqRF+Lr4MjpqdP1O2PFfSN4CE/6pDWIrmj53gGcr+PW1qx7q6+pLn5A+rDuzzgqB2Y+GJoqbpJT9pJRrAaSUG9AKGt0vhHjfnIEJIUJEzSitEKJfTay55nwOe7WhpkiRGp/Q35QeYaTll7H/bL5Zr5tTlsPGsxuZ0m4Kzg7OVz8h/QCs/7tWR7rnzWaNxe45ucGQR7QkenrLVQ8fEzWG0wWnOZV/ygrB2YeGDmYvruW+g8AgYERDriWE+BbYAXQUQqQKIe4UQtwrhLi35pBZQLwQ4iDwDnCDVCNMAPx6LIt2QR5EBbjrHUqLN65rK5wdDCw/mG7W6/6Y9CPVpmpmx8y++sGVJbD4LvAIhKn/bV67wppL79u0+tq/vqZtkFiHkZEjAVSr4iJXTRRCiDZXO0ZKmQIMFpp6jbpJKedIKUOllE5Syggp5Twp5YdSyg9rHn9XStlVStlDSjlASqm2dgSKK6rZeSqX0Z1b6R2KAni7OjGiYxA/HzqH0WSezzFGk5FFxxfRP6Q/bXyu+ucHq/8KuSdgxofNc1dYc3Byg6GPQso2OL25zkNbebSie1B31qWoRPG7+rQodggh5gkhBl7pACGEH3ADcASYZq7glMttTcqmyihVt5MNmdIjjKyiCnafNs9s723p20gvSee6jtdd/eDE5bD3Cxj8F612tHJlveaCVxhsuvrOsmOixpB4PpH0YvO2FO1VfRJFJ7T1Dj8LIXKEEKuFEJ8LIT4QQnwnhDgEZKHV0X5YSvmuJQNu6TYczcLL1ZE+0XZc57iZGd05GDcnB1YcMs+bysJjCwl0C2Rk1Mi6DyxMh2V/htA4GPk3szx3s+bkCoP+rLUqrrIH1O8TCNTiO81VE4WUMl9K+QQQDtwLJAK+QBugGvgS6CmlHCylVPUELchkkmw4ms2wmCCcHNSO7rbC3dmRMV1asSo+gypj/ctw1iatOI0tqVu4tsO1da/ENpngxz9BdYVWiMixHgPeirYFuauPtgdWHaK8o4jxi1HdTzXq/W4jpSyTUi6SUj4spZwhpRwvpbxZSvmmlLLW/ZoU84pPLyCnuILRalqszZnSPZTzJZVsP9m0iXmLjy9GCHH1Qezt72h97eNfh8AOTXrOFsXFE/rcqXXZ5Z6s89DRUaPZn7WfnLIcKwVnuxr8sVQIMUoI8YIQ4hlVe8K61idmIQSMUOMTNmd4xyC8XB2bNPupyljF4qTFDIsYVvd24un7YcPfofMU7ROy0jD97wUHJ9hRdy/56KjRSCQbz260UmC2q6Ers58D1qHVnrgLbc+nZCFEA7a1VBprw9Esekb64u+huhlsjYujA9d0DWF1fAYV1Y3bpnr9mfWcLz/PdTF1DGKXF8KiO7VtKaa8o6bCNoZXK+hxAxxYAMVX3vInxi+GSK9INU5B/abHPiqEGCmE8AceAh6QUraWUrYDWgEfAiuEEGMsHGuLllVYzuG0AjUt1oZN6RFGUUU1m441br+xhccWEu4ZzuDwwbUfICX89ADkJWvjEmoqbOMN/DNUl8Puj694iBCCMVFj2JW+i8JKy+znZS/q06KYA/wMZAN+wGQhxN+EEJMAVynl68AjwOuWC1PZeExbja227bBdg9oF4O/hzPJGVL47lX+KPZl7mB0zG8OVSs/vfB8Sl8GYFyH6CslEqZ+gGOg4CX77RFuweAWjW4+mWlaz6ewmKwZne+oz66kv4AX0ACrRpsqOAb4GzgohstC6oroLIa4TQnQW4kq/6UpjrU/MItTHlU4hXnqHolyBk4OBCbEhrDuSSWlldYPO/f749zgaHJnefnrtB6TsgDXPaVt0DPpz04NVtLUnZXmw/+srHtItsBvB7sEtfvZTvd7QpZTGmplNW4CTUsoRUko/oANwH7AXcATeBhKAK6dopcEqqo1sPZHDqE7BqkiRjZvSI4yyKiNrj2TW+5zSqlKWnVjG2NZjCXALuPyA4iz44Tbwaw3T31fjEuYSNQAi+mmD2sbaE7tBGBgTNYZt6dsorSq1coC2o6Gf/B8HHhJCfCWEGIy20G4DIIE0KWUYEAxMMG+YLduuU1qRItXtZPv6RfsT7uvGj/vT6n3OL8m/UFRVxPUdr7/8QWM1LLoDygvguq+0NQCK+Qx+CPLPQOJPVzxkTOsxVBgr2JJ29Q0Fm6uGbgp4COgFBAK/AgVADtpCvKdqjsmRUv5q1ihbuA1Hs3BRRYrsgsEgmBYXxubj2WQVldfrnO+PfU973/b0Cu51+YMbX9F2PZ38FoTEmjlahY4TIaC9tgDvCpsF9gruhb+rf4uuUdGYCnenpZQTgFC0fZ2uA9pJKReYOzgFpJSsP5rJ4PaBqkiRnbi2VzgmCcsOXH1NxcHsgyTkJjA7Zvbl3YpHV8LWf2s7n8bdaJlgWzqDQRvzOXfwipsFOhgcGBk5kk2pm6gwVlg5QNvQ6EHnmpbDCinlYillqjmDUv7nZHYxZ8+XMVJ1O9mN9sFedI/wqVf301dHvsLLyevyQezMI/DjvRDaA8ZffRM7pQm636CtS6ljW4+xrcdSWl3KjvQdVgzMdqjZSTbu9yJFanzCvszoGU5CeiHHMoqueMy54nOsS1nHzJiZuDtdVFukMB2+maVtjX39N9pmdorlOLlCv3vg5HrIOlrrIf1C+uHl5NViZz+pRGHj1idm0SnEi3BfN71DURpgSo8wHAyCJfuv3NhecFTrrb2x00XdSuUF8M1sbQX2TT+Ab73KuyhN1ed2cHCBXR/W+rCTgxMjIkew8exGqkxVVg5OfypR2LCC0ir2pOSp1oQdCvR0YXhMED/tT6+1oFFpVSmLjy9mTOsxhHqGandWV8LCWyD7KFw/H0K7WznqFswjEHpcDwe/g9La64qMaT2GwspCfsv4zcrB6U8lChu2OSkbo0kyurNKFPbo2l7hZBSWs/PU5TvK/njiR4qqirilyy3aHVLCsgfh9CaY9h60G2XlaBX63wfVZbD381ofHhQ2CDdHtxbZ/aQShQ3bcDQLP3cn4iLtuEhRRTEYW15THWBM51Z4uTiyZN+lg9pGk5FvEr+he1B3egT10O7c8Hc4tBBGPadtWKdYX6suWpXA3Z/U+jvr6ujK0PChbDizAaOpcRs/2itHvQNQaldtNLHxWBYjOwbjYLDxlbgmE5zbDzlJcP7UpbeyPO0YF29w8wP3AG0zO/cACOkG0UO1fw3Nb+qvq5MDE7uFsvxQOn+f3hV3Z+3PbVPqJs4WneUvvf6iHfjbPNjyJvS+HYY+pmPECgPuhwXXQcJS6H55TZCxrceyJmUNB7IP0LtVb+vHpxOVKGzU7uTz5JdWcU1XG94tNi8ZDnwLBxdoq1sBENoArH9b6DoDfKO0vvey81rfb2mudss6qn2CBm21cevBWtJoMxSCu2rz25uBGb3CWbjnLGsSMpneMxzQpsSGeoQyJmqMliR+fgxixsPEf6ntOfTWfqy2AG/ne9Bt1mU/j6ERQ3E2OLMuZZ1KFIr+1iRk4uJoYFhMkN6hXKqyBI78pO3ln7wFEFpzfeTfILyXlhgcXep3rcJ0SN4GyZvh9BY4tlK73zcK4m7SFpn5RlnqlVjF71t6LNmfxvSe4STmJrIncw+P9X4Uxy1vwcZXocM1MOtzcFB/jrozGLTCRisfh7O7Iar/JQ97OHkwKGwQ686s48m+T7aYvdfUb6YNklKy9kgmQzsEXuiu0J2xCna8B5v/BZVFWoth1N+gxxzwiWjcNb3DtOb97038glQ4tQkOfw+/vq7d2gyDnjdr1dyc7G+KsMEgmNEznPd/PUFWYTlfHfkKN0c3rk0+BHs+0/7/pv5Xq7im2IYec7Qxo53vX5YoQJv99GvqryTkJhAb2DK2VdGtfS+E+EwIkSWEqLXettC8I4Q4IYQ4JISoZSOc5ikhvZC0/DLGda2jHKY1peyAD4fCuhe0N+7bf4E/74NhTzQ+SdTGJwJ63gS3/gQPH4IRz2jdW0vuhn/FwMontXEPOzOjZkuPBXviWZW8ihl4473nMxj4IEx7XyUJW+PiCb3marU/LnSp/s+IyBE4CkfWpqzVITh96NkR/AUwvo7HJ6BtY94BuAf4wAox2YQ1CRkYBIzWe/1E6Xn46UH4fDxUFsOc72DOAmg90PJ96b5RMOIp+MsBmLsCOk7QPoG/0wu+u0lLXlfYxM3WtAvypEeED0uOL8Boquam0/thzEsw7pVmMxbT7PS7BxC1VsDzcfGhX2g/1qWsQ9rJ72BT6fZbKqXcjFYE6UqmAfOlZifgK4QItU50+lqdkEnfaH8CPOvZ129uUmpjEO/2gYPfalsxP7BLe7O2NoNBG+C+9mN4JF6bFZSyTUten46G+MVXrCVgS27oZKTaeS3DS8uImvg2DHlYDVzbMt9I6DIV9s7Xpnj/wZjWYzhTdIZjecd0CM76bPnjTDhw9qLvU2vuu4wQ4h4hxB4hxJ7s7MbVK7YVyTklHMss0q/bqaoMFt8JS+/TZn/8aTOMfRmcPfSJ52JeITD6OXjkCEx6S9vuYtEd8E4cbP+v9r2tkRL2fkF1wu0UOUCkxw3Q6xa9o1LqY8D9UFGgfVj6gzFRY3AUjqw6vUqHwKzPlhNFvUkpP5ZS9pFS9gkKsrFZQg30e2W0cV10mBZbnAVfTtE+pY9+QRuLaNXV+nFcjbM79L0THvgNbvgW/KJhzd/gra7wy18hL0XvCDUFqfD1TCpWPMTnvt4E0pavTw2lvKplLdayWxF9Ibw37PxAWyt0ET9XPwaEDeCX07+0iO4nW04UacDFO6JF1NzXrK1OyKBLqDeR/u5XP9icMhPgk1GQEa9VUhv6qO33nxsM0Gki3LYC7vlV6xrb/ZHWwvh+LpzZqc84hpSwbz68PxDO7GRR/1vIxsitsQ9SWF7NysPnrB+T0nBCaK2K8ychac1lD09oM4H0knQO5RzSITjrsuV3gmXArTWznwYABVLKZv0Xll1Uwd4zeYyz9iK742tg3jgwVcMdq7S+WXsT1hNmfgIPHYJBf4FTG+Gza+DdvrDlLSi0wq+OlJC6R9sifNmfIaQ7Ffds5LPCRHoF92Juz9G0CfRgwa7LZ9IoNqrLNPAO1xbg/cHIyJE4G5z55fQvOgRmXXpOj/0W2AF0FEKkCiHuFELcK4S4t+aQlcAp4ATwCXC/TqFazfrETKSEcV2sND4hJez8EL69XlsXcfcG7Q3XnvmEw9iXtHGMae+BRxCsfwn+3UXbvjthKVSbuUpZZQns/QI+GqYNsJ/ZCRPegLnL+TF3P1llWdwXdx8Gg4E5/SLZk5LH8cwr16lQbIiDE/S7W6t+l3HpTH4vZy+GRgxldfLqZr/3k26ruaSUc67yuAQesFI4NmF1QgaR/m50DvWy/JNJqb2Bbv03dJqszSqyhQFrc3Hx1Bbq9bwZck/CgW+07UZ+mAvOnhA1EKKHaNuGhPZo+KpoKSH7mDZl9+C3UFGobT0y6U3ofj24eFFprOTTw58SFxRH/xBt4dbMXhH8a/Vxvt19hhem2OD4j3K5XnNh0/9pYxXTL21ZjI8ez/oz69mXtY++IX11CtDybGTZr1JcUc22E7ncMrC1dbYF2PR/NfWYb9dmENn6eERTBLSD0c/DyGe1LqmjKyF5q7aAEP6XOMJ7a5sVuvmCq+///jU4QO4JLTHkHIPs45BzHMrzwcFZ657oexdE9r9kyuvSE0vJLM3k5UEvX/iZBni6cE1sCIv3pvLU+E64OjW/zRCbHXd/bbX2/q9gzAvg+b/1TcMihuHm6MYvp39RiUKxvE3Hsqk0mqwz22nbO/DrP6DHjc0/SVzM4ADtx2g30GZ5JW/93+1EPVbaegRBYIy24WGrrtq/HoGXHVZlrOLTw5/SPag7A8MGXvLYnH6RLD+YzsrD57i2lxlXtiuWM+A+2DNPa0GOePrC3e5O7oyIGMHalLU83f9pnAzNc5W9ShQ2YnVCBv4ezvSJ9rfsE+3+BNY+B12vhWnvtpwkURvPYIi9VruBtstteYHWUijL/9+/xkqtVRIYo326rIelJ5dyruQczw98/rIW4sC2ARcGtVWisBOBHaDDOPjtUxj88CV1zMe3Gc+q5FXsPrebweGD9YvRglrwu4TtqKw2sfFoFmM6W7j2xP6vtV0xO07SxiSaYQ2IJnF0Bs8g7U0hsi90GKttWNjzJogaUO8kUWWq4tNDn9ItsBuDwy5/4xBCqEFtezTgfijJ1tYZXWRI+BC8nLya9eI7lShswM5TuRRVVHONJVdjH16k7dvUbhTM/lxtRGdBy08uJ70knXt73HvF8aaZvSJwdjDw7W41VdZutB0BwV20XWUvWp/j7ODMyKiRbDizgUpjpX7xWZBKFDZgdUIG7s4ODG5/eV+3WRxbBUvu0YoDXf9N/etFKA1WZari40Mf0zWgK0PDh17xuIsHtdVKbTshhDZWkRlfU4vlfya0mUBRVRHb0rbpFJxlqUShM6NJsuZIJsNjgiwzA+bcQW0/pNAecON32vYXisUsOr6ItOK0OlsTv5vTL1Kt1LY33a7TZsbteP+Su/uH9sfXxZdVyc2z+0klCp3tPJVLdlEFk7uHmf/iRRnw7Rxw89e2CHexwvqMFiy/PJ93979Lv5B+DI8YftXjLx7UVuyEkyv0uROO/6Ktz/n9boMTY1uP5dezv1JaVapffBaiEoXOfjqQhqeLI6M7m7n2RFWZliTK8rWWhJcN195uJt478B7FVcU81e+peq2FUYPadqrvXdoY364PL7l7QpsJlFWXsTlts06BWY5KFDoqrzKyKj6Da7qGmLfbyWTStglP36/tfxTSzXzXVmp1PO843x//ntkxs4nxi6n3ebN6R+LsaOCL7cmWC04xL69WEDsL9n+jFfeq0Su4F4Fugc1y7yeVKHT067FsisqrmRZn5m6nTa9Dwo8w5kXoNMm811YuI6Xk/3b/H55OnjwY92CDzvX3cGZmr3AW7U0lp9jMe1ApljPoQagqgd/mXbjLweDANdHXsCV1C0WVzauFqBKFjn46kEagpzOD2gWY76KHF8Gmf0LczVplOsXiNpzZwK6MXTwQ9wC+rr4NPv+uoW2prDYxf4eN1NFQrq5VV2g/Vut+qiq7cPfktpOpNFU2uzUVKlHopLC8ivVHs5jcPQxHBzP9GFL3wNL7IWoQTP63KrVpBRXGCt7Y8wbtfdtzXcfrGnWNdkGejOnciq92JFNWqabK2o0hD0NpjrbhZI2uAV3p4NeBH5N+1C8uC1CJQier4zOorDaZr9upOAsW3qyVC73+a22VsWJx8xPmk1acxlP9nsLR0Pgdcf40vC15pVX8sPfs1Q9WbEPrwRDeRyvDW1O3XQjBjPYziM+N53jecZ0DNB+VKHSy7GA6Uf7uxEX6Nv1ixmr44XZthtMN34CHGbuylCvKLMnkk8OfMDpqNANCBzTpWn1a+9EzypdPt5zGaGr+pTWbBSG07t28ZEhcduHuyW0n42hwbFatCpUodJBVVM62EzlMiwszz5bi61+ElK1ad5Oa4WQ1/973b4wmI4/1eazJ1xJC8KdhbTlzvpRf4jPMEJ1iFZ0mQUB72Pb2hW09/Fz9GBk5khWnVlBlrNI3PjNRiUIHKw6ewyQxT7fTkZ+0pm+fOyGuzlpQihntydjDz6d+Zm7XuUR6RV79hHoY2yWE6AB3Pt58EqlHrW+l4QwOWundcwfh1K8X7p7Rfgb5Ffn8mvrrFU+1JypR6OCng+l0CfWmfXATV0pnH9cGr8P7wPjXzBOcclWFlYX8detfifCM4K5ud5ntug4GwV1D23IwtYBdp89f/QTFNvS4ATxbaa2KGoPCBhHsHsySpCX6xWVGKlFYWXJOCQfP5jO9ZxNbExXF2uC1owtc96Xa6M9KpJS8suMVskqz+Oewf+LuZN69s2b1jiDAw5mPN58y63UVC3J00TYLPPUrpB8AtDUV09pNY3v6djJK7L8rUSUKK1t2MB0hYEqPJiQKKWHZg5CbBLM+Ax9V/MZalp9azqrkVdzX4z66B3U3+/VdnRy4dWA0G45mkaS29bAffe4AF2/Y9p8Ld81oPwOTNLHs5LI6TrQPKlFYkZSSpQfS6BftT6iPW+MvtPMDbeX16Oe1PfIVqzhbeJZXd75Kr+BeZu1y+qNbBrbG1cmgWhX2xNUH+twOR5bCee3nFukdSd+QvvyY9CMmadI3viZSicKKEtILOZVdwrS48MZf5MwurZRpx0laSUbFKqpMVTy95WkchAOvD30dBwtWB/T3cOa6PpEsPZBGZmG5xZ5HMbP+94HBEba/e+GuGe1nkFqcyt7MvToG1nQqUVjRTwfScHIQTOzWyEp2JTnww21aV9P099XKayv66OBHHMo5xPMDnyfUM9Tiz3fnkDYYTZJPVKvCfniHQvfrtZXaRZkAjGk9Bk8nT7tfU6FrohBCjBdCHBNCnBBCPF3L47cJIbKFEAdqbpZr71tYtdHEsoPpDI8Jxte9EaumTUZYcjeU5sJ188HN1+wxKrXbm7mXTw5/wtR2UxnfZrxVnrN1gAfX9opg/o4UUvOaX32DZmvII2Csgq1vAeDm6MbENhNZm7LWrjcK1C1RCCEcgPeACUAXYI4Qoksthy6UUsbV3D61apBmtC4xi8zCCmb1buTA8+Y34OQGmPh/WrU6xSoKKwt5ZsszhHuG89f+f7Xqcz86NgYh4K01zWcriGYvoB30vAn2fAb52nYsMzrMoNxYbtcbBerZougHnJBSnpJSVgLfAdN0jMeivtyeTLivG2MaU6Do5Ab49XXoMQd6zTV/cEqtyqvLeWjDQ2SXZvP60NfxcPKw6vOH+bpx2+BofjyQxpH0Qqs+t9IEw57U/t38BqBtFNjet71ddz/pmSjCgYt3QEutue+PZgohDgkhFgkhal0CK4S4RwixRwixJzs72xKxNsnxzCJ2nMrlpgFRDd8ptiANFt8FQZ1g0ptqXMJKqkxVPL7pcfZm7uXVIa9aZCpsfdw/vD3erk68/stRXZ5faQTfSOh9O+z/GnJPIoTg2g7XEp8bT2Juot7RNYqtD2YvB6KllN2BtcCXtR0kpfxYStlHStknKCjIqgHWx5fbk3F2NHBD36iGnWisgkW3Q3UFXP8VOFv3E21LZTQZeXbrs2xK3cTfBvyNiW0n6haLj7sTfx7Vns3Hs9malKNbHEoDDX0MHJy12jDA1HZTcXd054uEL/SNq5H0TBRpwMUthIia+y6QUuZKKX8v+/Up0NtKsZlNQVkVS/alMbVHGP4eDRzEXvcinN0FU9+BwA4WiU+5lJSSf+z6B6tOr+LhXg83usaEOd0ysDXhvm68tioRk9pZ1j54tYL+98Ch7yHrKD4uPsyKmcXq5NWkFadd/Xwbo2ei+A3oIIRoI4RwBm4ALlnCKIS4eB7iVMDu2m2L9qZSVmXktkHRDTsxfjHseBf63QOxMy0Sm3K5/+z7D98f/547Y+/kzm536h0OAC6ODjx+TQwJ6YUsP5SudzhKfQ1+GJw9YeOrANzS5RYEgvkJ8/WNqxF0SxRSymrgQWA1WgL4XkqZIIR4WQgxteawvwghEoQQB4G/ALfpE23jmEySr3Yk07u1H7HhPvU/MTMBfnoQIgfAuFctF6ByiU8Pf8q8+HlcF3MdD/WyrTKy03qE0yXUmzdWH6OiWlXBswvu/jDwAa1WRfoBQjxCmNh2IkuSlpBXnqd3dA2i6xiFlHKllDJGStlOSvlqzX3PSymX1Xz9jJSyq5Syh5RypJTSrkb0NiVlk5xbyq0DW9f/pLI8+O4mbd+Y675UleqswCRNfHjwQ/6z7z9MbDORZwc8a546IWZkMAientCJ1Lwyvt55Ru9wlPoaeD+4+sLGfwBwe9fbKTeW892x7/SNq4FsfTDbrs3fnkyQlwsTYuu5ktdkgiX3QEGqtqjOq5EruJV6yy3L5d619/LegfeY1HYSrwx5BYOwzT+LYTFBDO0QyH83JFFQ1jwK4jR7rj5abe2k1XB2N+392jM8YjjfJn5LWXWZ3tHVm23+RTQDyTkl/Ho8mxv7ReHsWM//5k2vQ9IarbZEVH/LBqjwW8ZvzF4+m31Z+3hh4Au8NuQ1nAxOeodVp6fGdyK/tIp3NyTpHYpSX/3uAY8g2PB3AG6PvZ28ijyWnliqb1wNoBKFhXy1MwUHIbipfz2nxB5bpU2li7sJ+uq7U4mUkvLqckqrSimtKqWkqoTiymKKK4sprSq1++prRpORDw5+wF1r7sLDyYNvJn7DrJhZNtfdVJvYcB/m9Iti3tbT7E1RxY3sgrOHNl329GY4vppewb3oHtSdLxO+pNpUrXd09eKodwDNUUlFNd/vOcuEbqEEe7te/YScE1qXU2ic1RbVSSk5W3SWI+ePkF6cTnpxOudKzl34t6Sq5Irnujm6EeQWRJB7EMFuwdq/7sG09WlLB78OtHJvZbNvuhklGfxt29/YdW4Xk9tO5rkBz5m9+JClPTupM1uSsnns+4OsfGgo7s7qz9jm9bkT9n4BKx9H3L+LO2Lv4OGND7M2ZS0T2kzQO7qrUr9hFrD0QBpF5dXcNqgeg9hl+fDdjeDgpC2qc2pCnYo6mKSJE/kn2Ju5l72Ze9mXuY/ssv+tYvdy9iLMI4wIrwj6hfQjyD0IB+GAQHvD//2N3yiN5Jblkl2aTVZZFgm5CWSdzaLc+L/tsL2dvWnv254Ofh2I8Yuha0BXYvxicHLQr1snKS+JLxK+YOXplTgKR14e9DLT20+32YRWF08XR96Y1YM5n+zkn6uO8tK0WL1DUq7G0RkmvQVfTIRN/2TkmBeI9o7m8/jPGR893uZ/D1WiMDMpJfO3pxAb7k2vKL+6D66u1MqZnj8FtywB3wau3L6KKlMVO9J3sPL0SrakbqGwUtsvqJV7K/qG9KV3q950D+pOhGcEns6ejX4eKSWFlYWcyD/B8bzjJOUlkZSXxIpTKy60TJwNznTy70RsYCyxgbF0C+xGlHeURQeOpZT8lvEbnyd8zta0rbg5ujE7Zja3drmVCC/7rgo4sF0Atw+O5vNtyYzrGsLg9oF6h6RcTfRgiLsZdryLofv13Nb1Nl7c8SI7z+1kYNhAvaOrk7D3/uY/6tOnj9yzZ49uz7/8YDp//nY/b87uwcy6doqVEn68Fw59BzM+0gq0m4FJmtibuZeVp1eyNmUtBRUF+Lj4MDJy5IXkEOYRZpVPMFJK0orTSMhNID4nnsM5hzmSe+TCbA8PJw86+Xeis39nOgd0prN/Z9r4tMHR0PjPLxXGCo6eP8rh7MMsO7mMxPOJ+Lv6c2OnG7m+4/X4uvqa6dXpr6zSyKR3tlBRbWLVw0PxdrXtgXgFKMmFd/tAYAyVt/7ENT9OoL1vez4Z94nekSGE2Cul7FPrYypRmE95lZHRb27Cx82J5X8egoOhjjfjja9ps5xGPgvDn2zyc2eUZPD9se/56eRPZJVm4eboxsjIkUxsM5FBYYN07fa5mNFk5FTBKeJz4jmSe4TE84kcO3/sQteVi4MLkV6RhHiEEOYRRqhnKGEeYYR5huHm6IZRGjGajNq/NV+nFqcSnxNPfE48SXlJVEttgLCNTxtu7XIrU9pNwcXBRc+XbTH7zuQx64PtzOodwf/NUtvP24X9X8NPD8DU/zLPqYq3973NNxO/0W3jyd+pRGEl7/96gv/75RgL7u7PoHZ1dAXs/wZ+ul9rhk57t0mD1wezD/L1ka9Zl7IOozQyLGIYk9tOZljEMLsZpDWajCQXJpN4PpHE3ETOFp0loySD9JJ0CioK6nUNL2cvugZ0pVtgN7oGdiU2IJZWHq0sHLlteGP1Ud7beJJ5c/swunPLeM12TUr4YhJkHaH4T5uYuuZ2At0C+XbStxYtsXs1KlFYQXZRBSP/9SsD2wXwya21/l9rTm6Eb2ZB9BC4aZE2iN1AVcYq1qSs4ZvEbziccxgvJy9mdJjBnE5z7L7v/Y9Kq0ovzMSqNFZiEAYcDA44CkccDA4YhIEgtyCLj3fYsopqI9Pe3UZuSSVrHh6GX0M3n1SsL+sofDgEus3ml57TeGLTEzzd72lu6nyTbiGpRGEFzyw5xA97UlnzyDDaBl1hYDjzCHx2DfhEwh2rtFWbDVBhrGBJ0hLmHZ5HZmkm0d7R3Nj5Rqa1m2Y3rQfFMo6kFzLtva0Mjwniw5t7N7zuiWJ961+GLW8ib13OvSe/4WD2QZZNX0aweyOKm5lBXYlC/TaZQeK5Qhb+dpZbB0ZfOUnkntRaEs4ecNP3DUoSZdVlzE+Yz4TFE/jHrn8Q5hnGe6Pf46fpPzGn0xyVJBS6hHnz3OQurEvM4rmf4u1+UWSLMPRx8G2N+PlRnu3zBFXGKt747Q29o6qVmh7bRFJKXvn5CN5uTjw0+go1I7KPw/ypWgGiucvAp37dQyVVJXx39DvmH5nP+fLz9Avpx+tDX6dvSF+bn3etWN+tA6PJKqzg3Y0nCPR04bFxHfUOSamLs7u2tuKbmURteYe7u9/NewfeY3r76QwOH6x3dJdQiaKJ1idmse1ELi9O6YKPey3jDZlHtCSBgNt+hlZdrnrNkqoSvj36LV8kfEFBRQGDwwbzpx5/omdwT/O/AKVZeWxcDDnFFfx3g5Ys5ja0DopiXR3GwJBHYetb3BH0Oj97R/PqrldZMnUJro712NXBSlSiaIIqo4l/rEykbZAHNw2oZRX2uYMwfzo4usDc5VetUldaVXohQeRX5DM0fCj39biPbkHdLPMClGZHCMEr02PJLankxeUJBHg6M7l7mN5hKXUZ9RxkH8V5zbM8O/k17o5/l3nx83gg7gG9I7tAjVE0wdc7UziVU8KzEzvj9MfBw9S98OUUbUzi9pV1JonSqlK+iP+CCUsm8Pa+t+ka2JVvJn7D+2PeV0lCaTBHBwP/ndOTvq39eWThAVVr29YZDHDtxxAYw4C1/2BS+HDmHZ5HckGy3pFdoGY9NVJGQTnXvL2ZbuE+fHVnv0vHDM7shK9ngUeA1pK4wtYcxZXFLDy28MIYxMDQgdwfdz9xwXEWj19p/grKqrj+ox2cPV/Kd/cMpFtEw2bZ2av80kpScks5X1pJWaWR0kojZZXVlNR8LdD2y3J3cdD+dXbEw8UBfw9nIv3c8XDRqaPl/Gn4ZBQ5noFM9XOkS2BXPhn7idXGI9X0WDPLL63kuo92kJZXxtIHBtOhlZf2gJRwYAGsfBy8w+DWZeATftn5BRUFfJ34Nd8kfkNRZRGDwgbxp+5/olerXhaNW2l5MgvLufb97eSXVvLazO5M7dE8uqFMJsmpnBIOns3nZHYxKedLOZNbSkpuCYXlTdu6O9DTmUh/d6JqbtEBHsSG+9AuyMPy045Pb4GvprOwTU9eMWXySO9HuCP2Dss+Zw2VKMyorNLIzfN2cTi1gC9u78ug3zdjqyiCFY/C4e8heijMnAdel66SzSnLYX7CfBYeW0hpdSmjIkdxd/e7iQ1Uu38qlnOuoIwHF+xnb0oeN/WP4rnJXXB10m8FcGPkl1ay/0w++8/ms/9MHgfP5l9ICI4GQYSfG1EBHrT2d6d1gPYGH+jlgruzA+5Ojrg5O+Du7ICbkwMSKK2sprTSSHFFNSUV1ZRUGMkuruDs+VLtllfKmfOlpOeXYzRp75EujgY6h3oTG+5NbJgP3SJ86BTiXfdWPY3x26cYf36MpzoPZHV5Gk/0eYJbu95q3ueohUoUZlJlNPGnr/ay8VgW793Yi4ndakqcph+ARbdDXjKMeEYrUnLRUvz4nHi+Pfotq06vwiiNXBN9DXd3u5sOfnUPbiuKuVQZTfxr9TE+2nyKrmHevHdjL6IDPfQO64oqqo3sTc5jy4kctiRlk5BeiJRgENAxxJu4SF96RvnSM9KXNoGW+6RfZTSRnFNCQnohh9MKiE8rICG9kOIKLUl5ujjSq7UffVv70Sfan7hIX9yczZCEVzxK1Z55PNVlMGvLzvJk3ye5pcstTb9uHVSiMAOTSfL4ooMs2ZfGK9NjuXlAa62radeHsOY5rdThzE+1rYSBSmMlq5NX8+3Rbzmccxh3R3emtpvKzV1uprV3PepUKIoFrE/M5NHvD2I0Sf45szuTuteznruFSSk5mV3Cr8ey2JKUw67TuZRXmXA0CHpF+TGkQyD92vjTLdxHvzGEGiaT5Mz5Ug6czee35PPsSc7jWGYRoLVuYsN96N/Wn/5t/OkT7d+4XX2NVbDsL1QdXMBTbTqxllKe6vsUN3e52cyv5n9UojCDf6xM5OPNp3h0bAx/Gd1B26tl3Qtw/BeImQDT30e6+XE87zirTq/ixxM/cr78PNHe0czpNIep7aY2qeaDophLWn4ZDy7Yx/4z+VzXJ4L7R7TXpXVRVmlk56lcNh7LYuOxLM6e17afbxfkwdAOQQxpH8iAdgF46pwY6iO/tJJ9Z/L4LTmP3afPcyg1nyqjxCC0VfP92wTQv40/vVv7EeDZgJ2M939N1c+P82SwP+tcHCy6H5RKFE300aaTvLbqKLcOiOKluELE9ne0BOHohhz9PEc6DGdtylrWpqzlTNEZDMLA8IjhzOk0hwGhA9QqasXmVFabeHPNMT7bdppqk2R0p2DuGNKGgW0DLPb7ajJJEjMK2XEyl60ncthxMpeKahNuTg4Mbh/AiI7BjOgYRISf/W9JU1ZpZP+ZPHaePs/u07nsO5NPZbUJgDaBHvSK8qN3a+3WIdgTQ13jHJlHqPr+Fp5wKGC9hxvP9H2aG7uYP1nYbKIQQowH/gM4AJ9KKV//w+MuwHygN5ALXC+lTK7rmuZKFAVlVaw4lM6SfWnsT8nlmTYnucuwAtJ+I8MjgPgu49nvF8KGc9tJK07DQTjQP7Q/Y1uPZWTkSALcApocg6JYWlZROV/vSOHrXWc4X1JJl1Bv7hjShik9QnFxbFpfu9EkOZ1TzI6TuWw/mcuOU7nkl1YB0DbIg+ExQYzsGEy/Nv52N7jeUBXVRg6lFrA3JY+9KXnsS8kjt6QSAC9XRzqHetMl1JvOoV50CvGmY4jXpf8nFcVULf8Lj2dtYoOHO6OCejGh43UMixpptr3ebDJRCCEcgOPAWCAV+A2YI6U8ctEx9wPdpZT3CiFuAGZIKa+v67pNSRTVRhNbj6axZfcu0pP3EcRZ2nhkE+J0lmRRSLynL/Gubpw3ak1kR4MjA0MHXkgOzal6mtKylFcZWbo/jXlbT5OUVYyHswOdQr3pFOKl3UK1N6+L+9ullFSbJJXVJgrLq0jKLOZYRhHHMos4XnMrr9I+RYf7ujGoXQCD2gcwsG0gIT62sz2FHqSUpOSWaknjTB6J5wo5mlFEaaUR0AbtowO1WVxhvm6E+7kR7uNKl8zFLE/6DyvcXch2dMQNwXDPtoxvN5khXW/Cxcmt0THZaqIYCLwopbym5vtnAKSUr110zOqaY3YIIRyBDCBI1hF0YxPF/J9f5dv0bylxMFFoMGD8Q/NbIGjjE01sYDet7nNALDH+Mc22cprSMkkp2ZKUw9ojmRzLKOJoRuEl6xL83J0uJIdKo4na/hKDvFzo2MqLmFZedAr1on8bf6L83VUX7FX8Pkh+NKOQI+eKOJZRSGpeGen5ZeTVtMQA/ClkoCGecI+95HmfYZcH5Dk44G6STHboznO3LmjU89eVKPQcJQoHzl70fSrQ/0rHSCmrhRAFQABwyZ4EQoh7gHsAoqJqXwV9NSEBkYSmeuLvFkhEQAR+vq3x8WuLj3swfq5+tPdtrwajlWZPCMGwmCCGxQQBWuI4V1DO0QztE29aXhlODgacHQ04OxhwcdS+dndxpH2QJx1DvPBXhZMaxWAQRAd6EB3owfjYS2ejlVRUc66gjLT8ctLzyygu709Z1W0YKo1MLU6lsmAFZ4x7CQi8fIGvOejZopgFjJdS3lXz/S1AfynlgxcdE19zTGrN9ydrjrni5jV6lkJVFEWxV7ZauCgNiLzo+4ia+2o9pqbryQdtUFtRFEWxEj0TxW9AByFEGyGEM3ADsOwPxywD5tZ8PQvYUNf4hKIoimJ+uo1R1Iw5PAisRpse+5mUMkEI8TKwR0q5DJgHfCWEOAGcR0smiqIoihXpuuRRSrkSWPmH+56/6OtyYLa141IURVH+RxUuUhRFUeqkEoWiKIpSJ5UoFEVRlDqpRKEoiqLUqdntHiuEyAZSGnl6IH9Y9d0CqNfcMqjX3DI05TW3llIG1fZAs0sUTSGE2HOllYnNlXrNLYN6zS2DpV6z6npSFEVR6qQShaIoilInlSgu9bHeAehAveaWQb3mlsEir1mNUSiKoih1Ui0KRVEUpU4qUSiKoih1apGJQggxXghxTAhxQgjxdC2PuwghFtY8vksIEa1DmGZVj9f8qBDiiBDikBBivRCitR5xmtPVXvNFx80UQkghhN1PpazPaxZCXFfzs04QQjSubqYNqcfvdpQQYqMQYn/N7/dEPeI0FyHEZ0KIrJrCbrU9LoQQ79T8fxwSQvRq8pNKKVvUDW1L85NAW8AZOAh0+cMx9wMf1nx9A7BQ77it8JpHAu41X9/XEl5zzXFewGZgJ9BH77it8HPuAOwH/Gq+D9Y7biu85o+B+2q+7gIk6x13E1/zMKAXEH+FxycCqwABDAB2NfU5W2KLoh9wQkp5SkpZCXwHTPvDMdOAL2u+XgSMFvZdGf6qr1lKuVFKWVrz7U60ioP2rD4/Z4C/A/8Eyq0ZnIXU5zXfDbwnpcwDkFJmWTlGc6vPa5aAd83XPkC6FeMzOynlZrT6PFcyDZgvNTsBXyFEaB3HX1VLTBThwNmLvk+tua/WY6SU1UABEGCV6CyjPq/5YneifSKxZ1d9zTVN8kgp5c/WDMyC6vNzjgFihBDbhBA7hRDjrRadZdTnNb8I3CyESEWrf/Nn64Smm4b+vV+VroWLFNsjhLgZ6AMM1zsWSxJCGIC3gNt0DsXaHNG6n0agtRo3CyG6SSnz9QzKwuYAX0gp3xRCDESrmhkrpTTpHZi9aIktijQg8qLvI2ruq/UYIYQjWnM11yrRWUZ9XjNCiDHAs8BUKWWFlWKzlKu9Zi8gFvhVCJGM1pe7zM4HtOvzc04Flkkpq6SUp4HjaInDXtXnNd8JfA8gpdwBuKJtntdc1evvvSFaYqL4DegghGgjhHBGG6xe9odjlgFza76eBWyQNaNEduqqr1kI0RP4CC1J2Hu/NVzlNUspC6SUgVLKaCllNNq4zFQp5R59wjWL+vxuL0VrTSCECETrijplxRjNrT6v+QwwGkAI0RktUWRbNUrrWgbcWjP7aQBQIKU815QLtriuJylltRDiQWA12oyJz6SUCUKIl4E9UsplwDy05ukJtEGjG/SLuOnq+ZrfADyBH2rG7c9IKafqFnQT1fM1Nyv1fM2rgXFCiCOAEXhCSmm3reV6vubHgE+EEI+gDWzfZs8f/IQQ36Il+8CacZcXACcAKeWHaOMwE4ETQClwe5Of047/vxRFURQraIldT4qiKEoDqEShKIqi1EklCkVRFKVOKlEoiqIodVKJQlEURamTShSKoihKnVSiUBRFUeqkEoWiKIpSJ5UoFMWChBCzhBAVFxeCEkL8RwhxUgjRSs/YFKW+1MpsRbGgmjomvwH7pZR3CyEeB54EBkspk/SNTlHqp8Xt9aQo1iSllEKIvwI/CyFOAn8FRqskodgT1aJQFCsQQmxHq8Y2RUpp70WhlBZGjVEoioUJIUYBPdBqGGfqHI6iNJhqUSiKBQkhegCbgUeASYCnlPIafaNSlIZRiUJRLKRmptMO4EMp5ctCiFjgEDBKSvmrrsEpSgOoRKEoFiCE8Ae2AZullH+66P6FQJSUcqBuwSlKA6lEoSiKotRJDWYriqIodVKJQlEURamTShSKoihKnVSiUBRFUeqkEoWiKIpSJ5UoFEVRlDqpRKEoiqLUSSUKRVEUpU7/DwvwJUUJu9u4AAAAAElFTkSuQmCC\n",
76 | "text/plain": [
77 | ""
78 | ]
79 | },
80 | "metadata": {
81 | "needs_background": "light"
82 | },
83 | "output_type": "display_data"
84 | }
85 | ],
86 | "source": [
87 | "t=np.linspace(0.0, 1.0, 51)\n",
88 | "\n",
89 | "hbar=1 # in atomic units\n",
90 | "mass_e=1 # in atomic units\n",
91 | "\n",
92 | "h=2*np.pi * hbar \n",
93 | "\n",
94 | "E1=1**2 * h**2/(8*mass_e*L**2)\n",
95 | "E2=2**2 * h**2/(8*mass_e*L**2)\n",
96 | "w21 = (E2-E1)/hbar\n",
97 | "\n",
98 | "def phi(t):\n",
99 | " phi=np.zeros(51)\n",
100 | " phi=(f1**2 + f2**2)/2+np.cos(w21*t)*f1*f2\n",
101 | " return phi\n",
102 | "\n",
103 | "plt.plot(x,phi(0))\n",
104 | "plt.plot(x,phi(np.pi/2))\n",
105 | "plt.plot(x,phi(np.pi))\n",
106 | "plt.legend(['t = 0','t = $\\pi$/2','t = $\\pi$'])\n",
107 | "\n",
108 | "plt.xlabel(\"$x$\", fontsize=14)\n",
109 | "plt.ylabel(\"$\\phi(x,t)$\", fontsize=14)\n",
110 | "plt.savefig('PIB_2.png') \n",
111 | "plt.show()"
112 | ]
113 | },
114 | {
115 | "cell_type": "markdown",
116 | "id": "b8f13e56",
117 | "metadata": {},
118 | "source": [
119 | "# Time-evolution movie"
120 | ]
121 | },
122 | {
123 | "cell_type": "code",
124 | "execution_count": 3,
125 | "id": "43bf89b5",
126 | "metadata": {},
127 | "outputs": [],
128 | "source": [
129 | "import os\n",
130 | "import imageio\n",
131 | "filenames = []\n",
132 | "for it in range (100):\n",
133 | " t=it*0.01\n",
134 | " \n",
135 | " plt.plot(x,phi(t))\n",
136 | "\n",
137 | " plt.xlim(0, L)\n",
138 | " plt.ylim(0, 3.5)\n",
139 | " plt.xlabel(\"$x$\", fontsize=14)\n",
140 | " plt.ylabel(\"$\\phi(x,t)$\", fontsize=14)\n",
141 | " plt.text(0.2,0.15, r'$t=$ {0:10.3f} [au]'.format(t), fontsize=12)\n",
142 | " \n",
143 | " filename='_tmp_'+str(it).zfill(5)+'.png'\n",
144 | " filenames.append(filename)\n",
145 | " plt.savefig(filename)\n",
146 | "\n",
147 | " plt.close()\n",
148 | " \n",
149 | "# build animated gif\n",
150 | "with imageio.get_writer('PIB_t.gif', mode='I') as writer:\n",
151 | " for filename in filenames:\n",
152 | " image = imageio.imread(filename)\n",
153 | " writer.append_data(image)\n",
154 | " \n",
155 | "# remove temporary files\n",
156 | "for filename in set(filenames):\n",
157 | " os.remove(filename)"
158 | ]
159 | }
160 | ],
161 | "metadata": {
162 | "kernelspec": {
163 | "display_name": "Python 3",
164 | "language": "python",
165 | "name": "python3"
166 | },
167 | "language_info": {
168 | "codemirror_mode": {
169 | "name": "ipython",
170 | "version": 3
171 | },
172 | "file_extension": ".py",
173 | "mimetype": "text/x-python",
174 | "name": "python",
175 | "nbconvert_exporter": "python",
176 | "pygments_lexer": "ipython3",
177 | "version": "3.9.4"
178 | }
179 | },
180 | "nbformat": 4,
181 | "nbformat_minor": 5
182 | }
183 |
--------------------------------------------------------------------------------
/notebooks/NumQM_Basic_03.ipynb:
--------------------------------------------------------------------------------
1 | {
2 | "cells": [
3 | {
4 | "cell_type": "code",
5 | "execution_count": 1,
6 | "id": "0fdaf173",
7 | "metadata": {},
8 | "outputs": [
9 | {
10 | "data": {
11 | "image/png": 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\n",
12 | "text/plain": [
13 | ""
14 | ]
15 | },
16 | "metadata": {
17 | "needs_background": "light"
18 | },
19 | "output_type": "display_data"
20 | }
21 | ],
22 | "source": [
23 | "import numpy as np\n",
24 | "import matplotlib.pyplot as plt\n",
25 | "import cmath\n",
26 | " \n",
27 | "L=1.0; dx=0.01; N=int( 2*L/dx + 1 )\n",
28 | "\n",
29 | "x=np.linspace(0, L, N)\n",
30 | "psi_1=np.sqrt(2/L)*np.sin(1*x*np.pi/L)\n",
31 | "psi_4=np.sqrt(2/L)*np.sin(4*x*np.pi/L)\n",
32 | "psi_10=np.sqrt(2/L)*np.sin(10*x*np.pi/L)\n",
33 | "\n",
34 | "plt.plot(x,psi_1**2)\n",
35 | "plt.plot(x,psi_4**2)\n",
36 | "plt.plot(x,psi_10**2)\n",
37 | "plt.xlabel(\"$x$\", fontsize=14)\n",
38 | "plt.ylabel(\"$|\\psi(x)|^2$\", fontsize=14)\n",
39 | "plt.legend(['n=1','n=4','n=10'])\n",
40 | "plt.savefig('psi_x.png') \n",
41 | "plt.show()"
42 | ]
43 | },
44 | {
45 | "cell_type": "code",
46 | "execution_count": 2,
47 | "id": "d805a8d1",
48 | "metadata": {},
49 | "outputs": [
50 | {
51 | "data": {
52 | "image/png": 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4FHCaMeYU4G+Bb4rIe+33qv8K6kBEvMDNwAXAicClZUThe8aYk2xbbgC+1Kz+ldnDvoR1l39S/0mA5Xm0nMQBaxtZCNEj6rpAJzK5miOnAEL+OsNTsb3Q1QfBKPi7IH7A/bENciBp9XHiwhPxiKc9oUGlo6j9TQa/MWYvgDHmCRE5B7hbRI4FmpmBPB3YYox5EUBE7gTeCWx0GhhjRkvadzW5f2WW4IjG0b1HE/FFiq9bSnzI2kYWWp7GrqdcH5rI5KvO0XCIBOoMT8X2W7YAdC0cF7YW4nh5R3YdSV+orz2CrXQUbjyNfSJysvPCGHMQeAtwAnByxaPqZwlQGpQdtPdNQEQ+JCJbsTyNfyj3QSJyhYisFZG1+/e33mVX2su+xD6C3iA9gR76I/3Fu9+WkhiCQDf4gtDVb12wXZLMVK+l4RAJ+Oqr3Bfba3k9YNnUxvBUX7iP+aH5DKeGW96n0lm4EY3/DUy4lTPGZIwxlwLntsSqKhhjbjbGHAN8HCt0Vq7N140xq40xq/v7+9troNJy9if30xfuQ0ToDfYynB5ufaeJA9bdPEB4vjXBL+/uAp9wKRohv5dUto51rRJDlucDEOlrW3iqN9hLwBtgXmgeh9KHWt6n0lnUFA1jzKAxpmzg0hjz+ybashNYWvJ6wN5XiTuBdzWxf2WWMJIeYX5wPgDzgvPaJBolF+jQPGubGnF1aDJbvT64QyTgJZMvkMu7FI7UyLgtXf1tEY2h5BB9oT4AFgQXcCilojHX6KR5GmuA40RkpYgEgEuAe0sbiMhxJS//HGtUlzLHGM2M0hvsBdooGvED1t08QHietXUZmkm6zGnUVb2vUID0qDUbHCCywBK2FjOSGRk/9+ppzEncJMIBEJGXaCzx/J/GmJtqNTLG5ETkauABwAt8yxizQUQ+C6w1xtwLXC0ibwaywCHgsgbsUWY5I+kRBqIDgCUaI2l3d/zTIjEER1hDfIt39y6XJLdGT0VqtguXVO/rDvmrN87EwBTGRSM8z1pMMZsCf8iVXY0wlhnjyMiRAMwPzWcsM0a2kMXvqWGvctjgWjSAyxvsY5vbhsaY+4H7J+37dMnzDzdog3IYMZIZocdeA2pecB7JXJJULkXI17qLJYmD1t08lHga7u6ykxl34am6PA0nNOaIhrNNjbRUNEbToxw3z3L4nRDhSHqEvnBfy/pUOgvXomGM+W0rDVEUNxRMgbHMGD0BWzTsu/7h9DBH+o5sTaf5LOSS44sV1utpZN2OnrLauJrgN0U05o3v7z7ClV2NMJoZHRdsu89DqUMqGnOIhnMaIhK08w8niogOUVLaQiwbo2AKE3IaQGtDVGm7bkcwam3D1h2225xGwq2nMS3R6J24vwXkC3li2VhRsJ1t2+uaKDNKXaIhIt0icpWI/A4YAbYA64E9IvKyiNwqIq9thaGKAlZ4BCiKhnPhGs2MVjxm2mRi1jbYbW2d8JQLTyNfMGRyhWIN8Go44SlXNTVmQDQccXDOebffOh+xbKxlfSqdh2vREJFrsPIT/wd4EGu29inAK4DXAddhhbseFJFfTBrppChNYSRjXRSdC1c0YN39xzItvHCl7c+2+8IXBF/Ylacxvix67Z+as9TI9MJTtW1qFEc0ugPdE7YtFWyl46gnEX4mcK4xZn2F9/8EfEtErgT+Dmvinw6JVZqKE4ZyPI2o3xaNVt7tTvY0nOfp2mEZZ4Z32MXaU46wuEuED1vbNnoajji0VbCVjqOeRPh7XLZLA7c0bJGiVGHKhasdouGIg+NpgJXfSNfu01lLKuJmnoYtLEk3S4k44lBMzrdeNIpent2n42loTmNuUY+nMQERCQL2msxsMsa0p9akMqeZnNNwLlwtvdstehqlouHW03BXgAlKhty6DU8FusFr/4T9IfAG2+ppBL1BAp4AY1kVjblEQ6OnROQtWIsLPgk8BQyJyDdEZFEzjVOUyTgXLkcsAt4Afo+/tReuyTkNsC7YLoTKbalXKBly6zYR7ngXDqHe1opGeuK5d56rpzG3aHTI7VeA3wLHAYuA99rPnxSRlU2yTVGmkMgm8IiHkHd8Alt3oJt4Jt66TsvmNKKuPI1ieMpFTiPo8yACKTeeRnp0oj1gi8Zw7WMbZPLoKbDOveY05haNisYy4BPGmBeNMQeMMT81xpwLPAx8uXnmKcpE4tk4Xb4uRMbrf3X5u1rsadijg0ov0gF3ouGEp9ysPSUihP0uq/dlEhDomrjPZcisUeLZOB7xEPaFi/u6A90anppjNCoaz1Km1gXw/4A3Nm6OolQnno0T8U9cxynqj7Z+yK3Hbw21dQi6C0+Nj56qLRpgF2JyE57KxMuIhrvkfKMkcokpgh31RzU8NcdoVDS+B3xFRI6ZtL8fayFBRWkJiVyCLv/Ei2V3oJt4tsXhqdIkONQ/esqlaIT8Lqv3ZeITcyzgOs/SKIlsgrA/PGFfNNBiwVY6jkZHTzm1uZ8TkfuwkuEe4FLgn5phmKKUI5GdKhpd/i4GY4Ot6zQdsy7IpQS6rfWo8rnxEUxlqGf0lNPOXXgqVsHTaG14avK57wn0qKcxx2hUNPqxZoM7j78GXgkI8BkR+UtgHbDOGPM/07ZSUWzi2TgR38TwVMuTsZU8DbAq+DlrUZWhntFTYOU+Gg5PucyzNEoil5hy7qP+qC4jMsdoSDSMMUPAr+0HUJy38SrGheQC4J+BedO0UVGKxHNx5ocmXqS7/F2tn9w3ORTkJMXTseqikcnj9QgBr7tIcDhQT3iqjKfR4vDU5HxSxB8hmUtSMAU80kk13ZRW0fDkvsnYM8GfsB+K0hLKhaei/ijxbBxjzIQkbdPIxMbXdnJwRKTGRTphV+1za1fY7+VALFO9UaEA2Qo5jXwGchnwBVz1Vw+JXKJYgMnB+V8ksonisiLK4U09Cxa6nn8hFktrt1SU+qiU0yiYAql8ixYlSI+VCU91j79XhWQ25zo0BdZ8jkStZUSyCWtbztOAlnkb8Wx8SiLcGX6byCVa0qfSedTjTz4mIt8UkddVaiAi80XkKmAj1iq4itJUyuU0nJBJItuiC1fZRLh9ga4hGomMuwJMDuGAl1S2UL1RUTQmlZB1aVOjVBJsoLWj15SOop7w1PHAJ4GfiUgBKwy1C0gB84ETgROwVrv9R2PMA022VZnjZAtZMoXM1Li6LSKJXIKFLGx+x1UT4dXv6pN2eMot1uS+Gp6G0+eUPEtrPY1yifDS8JQyN3DtaRhjho0xH8Oa1Hcl8BxWknslkANuA15jjPkzFQylFTgXpsl3uy31NIyxh7c2Gp6qz9NwNbnPWTJlyuipkuR8k8kX8iRzyannvkSwlblB3YlwY0wS+JH9UJS2UVE07AtXMpdsfqfZBJjCVE+jmAivfrF0W+rVIeS3wlOFgsHjqZA8ryQajpC1YN6Ec24reRoanpo7TGdp9DcCZwMZ4FFjzCNNs0pRyuBcmMoN+4QWeRrOXfvkxQEdG1yMnpofcT+SyfFKktk8XcEKP89a4akWeBqOJ1Hp3KtozB0aXRr9X4FfYZV+fT/wkIhsE5FzmmmcopQSz9miMTkR3soQSfECPVk0woCMJ6UrkMzk6k6EQ43qfRXDU63LaTiCXC2fpMwN6qoRLiLnicgC4MPAh4wxy40xxwBHAF8F/kdE3twiW5U5jnM329a4enGF20l39SLWRdtFeKou0XBTiKlWeKoFnoYj2F2+8qOnNBE+d6gnPHUp1iq2zlKffyEiC7HWnXrKGPMFEdkPfAFY3VwzFQWSWSuu3tZEeLkCTA7+iDXJrgrJbH05DafuhjtPo1Kepfk5jUqehjNPQ8NTc4d6Rk+9FugGXo2VxzgIvBm4A9ghIvuwwlUni8h7ROQEEV1XQGkele52i6LRyvDUZE8DrHkSNYo/1T3kNmD9ZKouWuj0OekCji8A3kBrchoVBiF4PV7CvrB6GnOIui7qxpi8MWY98Aiw1RjzBmPMfKyqfVdhzd3wAf8JbAD09kNpGpUS4SFvCEFa7Gl0T30vEK0ansrkCuQKpnJCuwxhv+1p1BQNsfMqZWxqweS+YiJ8Uj7J2ecIunL40+joqY8Cv7XraXwVeAZ4CDgH2GmMWSoifVgLGCpKU6gkGiJCxB9pkadhX4Anj56CmuGpYgGmujwNJxFeZYKfU0uj3HpWLVq0sNK5d/ZpeGru0Ogqt+tE5FTgFuA3jHssOeBv7TYH7PcUpSmUqw/uEPFFWjzktv7wVL21NErbJjNVlhIpV0ujaFN3S8NT5USjy99VzDcphz8N5xyMMS8ZYy4AjgLeBbwHOMYY871GPk9EzheRTSKyRUSuLfP+NSKyUUTWicivRWR5o7Yrs5Ny5UYdIv4WiYZz1+4vc5GuEZ4qikZd4SmvfWwtT6OCaASjLUmEVxru7OzT8NTcYdqJamPMfmPMfcaYHxtjGiqfJiJe4GasGhwnApeKyImTmj0FrDbGnIw1G/2G6ditzD7K1Qd3iPhaFJ5K20uIeMr8VGqEp4qlXhsKT9XIaVT0NFpTJzyZTRL0BvF5pgqghqfmFq5vgUTkJcA00Md/GmNuqtHmdGCLMeZFu687sVbJ3eg0MMY8XNL+j8D7GrBFmcWUKzfqEPaFWzdPo1KdiECkqqcRt72FxsJT1USjzFpYDsEojOxw3Z9bqp37Ln8Xg2MtLLerdBT15DQub7CPbS7aLAFKv+mDwBlV2v8d8PNKb4rIFcAVAMuWLXPRvTIbKLfKqkPEH+FQ6lDzOy23wq1DIFo1p5FsIDwV8jnhqRqeRqTCar6tymnkEsU5GZPp8nfpkNs5hOtvszHmt600xC0i8j6syYPnVmpjjPk68HWA1atXN+IdKR1IuXoODl3+LnbGdja/03Ss/MgpsMNTCWsl3DJ5lkYS4R6PEPJ7SFULT2UTEKhQ4yxYXcgapdq515zG3KJTJt/tBEp/BQP2vgnYS5R8ErjQLi+rzCFq5jRalQivFp7CQIWRQ/EGhtw67Wt6GhVtshPhprn3SvHc1OJXDs4gBNPkPpXOpFNEYw1wnIisFJEAcAlwb2kDEXkN8DUswdg3AzYqM0y1uHrL5mlU9TRsWyrc2Scb8DSs9r4aifBqQ267rKXcmzwENpmdWkvDIeKLYDCtWZpe6Tg6QjSMMTngauABrOJOPzDGbBCRz4rIhXazLwJR4Ici8rSI3Fvh45TDlES2Sk7DFyGZTTb/bjczVuWu3r6IVhg55HgL9cwIBwj5PbVnhFcccuvU1GhuXqOal1dctFBXup0TNFxPo9kYY+4H7p+079Mlz3X13DlOIlclru6PkDM5soUsAa/7+hU1SVdLhDs1NcpfLBOZHCIQ9NV3b1bV08hlIJ+pPuQWrKVEoovq6rca1QYhTFjptnyuXDmM6AhPQ1FqkSvkSOfTFe92nZE9Tc9rpKt4Go6AVegzkckT8XvLTkasRtU64Y5XU23ILbTV03DEROdqzA1UNJRZQaVaGg4tqamRz0I+XTmn4dztV7hAJzL5uobbOoQD3srhqUq1NIo2taZ6Xy0vD1Q05goqGsqsoNLS3A4tqamRrrJYIdQMT9Vbtc8hEvBWDk/VEo0W5DSy+Sy5Qq52eEpzGnMCFQ1lVlBtae7S/U2dL1CpFrdDjfBUvM5aGg5Vh9wWa2m4yGk0iUr1wR20et/cQkVDmRVUW5obWnThqrbCLdQMTyUz+bpHToEVnqo4ua+mpxGd2K4JFFe4reFpaHhqbqCiocwKauY0WlG9r+hpNBaeSjQYnnLlaQTKX8DHS742LzzlnNNwuaJPaMnXuYaKhjIrqJnT8LUyp1ErPFV5nkYj4Sknp1F2zkmtkFkLEuGuPQ1dSmROoKKhzAqcu93J9cEdWpoIr3SB9gXA46/iaeQb8jRCAS/GQDpXphCT8/dVCk95feALN7WmRq18ks/jI+gNaiGmOYKKhjIrcEIflUIkLRly69zVVxo9BVWr9zU65Napv1F22G0xEV4hPAWWoLTC06jSZ5e/S8NTcwQVDWVWUCunEfaFEaS5F660C9Hwd1UJT+XqKsDkEAlYQpMolwzP1JjcB02vE17L0wDr/Gt4am6goqHMCuLZeMX64AAi0vxFCzM1wlNQsRCTMYZktvHwFFTxNDw+KzRW0abm1tSoNeQW1NOYS6hoKLOCZC5ZsT64Q9OXR0/HwBuocYHuKjtPI5UtYEx9BZgcqoansonK+QyHZnsaNRLhYImG5jTmBioayqwgno1XzGc4OHUdmka1WhoO/q6yOY1EA6VeHZw64WXXn8rEKk/scwhEWzK5r1LlPtA64XMJFQ1lVlCtloZDxNfk8FS1FW4dKiTCnXkWDc0Id8JTZXMa7fc0ktkkIW8Ir6fy36LV++YOKhrKrCCei1ccbuvQ9JxGegyCPdXbVAhPNVpLA8aFpmJOo9LEvqJNzS35msglquYzQHMacwkVDWVWUK1ynEPTL1zVCjA5VAhPFUu9NrhgIVB+Vng2UdumYJMT4dlE1dAUaE5jLqGiocwKXOU0WpEIbzA8FUtZotHdgKfheCeVcxpuPI1Y0+qEu/E0nPCU1gk//FHRUGYFrnIaM5EIrxCeiqetC340VL9oRG3RGEuXEw2XOQ1M00JU1crsOkT8EQqmQCqfakqfSueioqHMChK5RO2cRksS4VUm9oEVnsqloDAxlORc8KMNeBpBnwe/V4reygSq1Qd3aPKihdVKvTro8uhzBxUNZVaQyFauHOfgJMKbFiJJj9UWjeLy6BPv6p0LfiOiISJEgz5i5TyNbB2i0aS8httEOKhozAVUNJSOJ1fIkcqnXOU0mhYiKRSsRHiDouGEpxoZPQVWWKuip1Erp1GsqdGcuRpuwlOOF6jDbg9/VDSUjqfWCrcOTb3bdUZh1RSN8qGgWDpnh5ka+4lFg/6pOY18FvIZF3mW5noayVyypqfhCLoOuz38UdFQOp5atTQcmlqIqday6A7ByqLR3UAS3CEa9E71NGoVYKphU6PEs3HNaShFVDSUjse1aDSzEFOxAJPL8FR6qmg0GpoCyuc0atXSKNpk29yE0VO5Qo50Pl0zNKjhqbmDiobS8dSqD+7QXE/DxbLoUBKemprTaCQJ7hAN+Yt5kSLFWhpuhtzSlPWnkjlrwp56GoqDiobS8Th3rzXnCjTV0xi1tg3mNMZS0/c0puQ0iuGp9g25dVOAqfR9zWkc/qhoKB1PrQJMDk29cNUbnpp0gY5ncg3NBnfoLjd6ym1Oo4mJcDcFmKBF5XaVjkRFQ+l43OY0iiGSZoSnHBFwmwifnNNogqeRzObJ5UvqhBdzGjVs8njsNbHaJxp+j5+AJ6A5jTmAiobS8bgOkfha4WnUWOXWX2FyXzrX0BIiDk4+JJ4umWnuiECteRpgiVkTchpuzz1Yoq2exuFPx4iGiJwvIptEZIuIXFvm/XNE5EkRyYnIxTNhozIzuM1pOJ6Gk7ydFsWcRo27eq8PfOEpE+li006EO+tPZcd3ZlyOnoLxRQunidtEOGghprlCR4iGiHiBm4ELgBOBS0XkxEnNXgYuB77XXuuUmcapD15reW6/x49PfE1KhDulXoO12wYmLo+eyxdIZQvTEw372AnDbt0mwp02zchp1OFpNH3BSKUjafxb3VxOB7YYY14EEJE7gXcCG50Gxpht9nuFch+gHL44y1hUqw8O1ppNYX+4eeGpWklwh2B0wgXaCSk1RTRKk+HZOkQj2N3UnEYtwQZrrobmNA5/OsLTAJYAO0peD9r7FMXVKqsOXf6u5s0Ir5VwdphUKc8JKTUjPDXV0xDwhVzaNH3RcDtyzWmjnsbhT6eIRlMRkStEZK2IrN2/f/9Mm6NMk1gm5io8Ak0sxJSJ1U6COwSiE3IaY04BpmkkwrvLhqfsWho1PC5givfTKLGs9RluRENzGnODThGNncDSktcD9r6GMMZ83Riz2hizur+/f9rGKTNLLBujJ+DuAu5UkJs29YSnJuU0RpKWp9Eb9jfcfdHTKA1PuVl1t2hTczyNWCZG2BfG56ktgE2vZ6J0JJ0iGmuA40RkpYgEgEuAe2fYJqVDiGViRF2GippWqzo9WnvklMOku3pHNHqmIxpO9b5S0agrz9KcOuHxbJyo3/25V0/j8KcjRMMYkwOuBh4AngN+YIzZICKfFZELAUTktSIyCLwb+JqIbJg5i5V2MpoZpTvg7mIZ9oebt/ZUXXf1TfY0gj68Hil+lmVTnXmWbNyqCzINYtmYq9AUjOc0tE744U2njJ7CGHM/cP+kfZ8ueb4GK2ylzDFi2Zjru92Ir0lx9bou0F0TchqjTfA0RITesH+SaNQhZKXLo4dc5mbKEMvUce79EfImTzqfJuQmWa/MSjrC01CUasQyMdeeRlNG8BgDqWEIz3PX3vE07DvskWQWEaa19hTAvLCf4cmehlvRCPVa29TItGyIZesLDTrHKIcvKhpKR5PNZ0nlU65FoynJ2GzSqpAXmueufaALCjnIpQFLNHpCfjweF6OcqtAb8TOcyIzvSI+5H9Hl2J4anpYN9eQ0nMEKY00qM6t0JioaSkczlrUuQK6TsYEukrkkuUKZ+tpucS60zt16LYITix6NJLPTymc4TA1P1ZGcd7yk5PC0bKgnp+GIxmhmdFp9Kp2NiobS0cTsYaNuPQ3nwjWtvIYT0nEdnnIWLbQErlmiMS/sZzhhi4YxdYan5lnb5KFp2VBPaNBpN5pW0TicUdFQOhon1NHWC5dzd+46PDWxel/TRCMSGA9P5VJg8u5FwxG8aYSnCqZAPBt372kE1dOYC6hoKB1NveGpbr8tGtlpXLicC209iXAozotoZnhqNJUjXzDui0I5FD2N4Yb7T+aSGIzmNJQJqGgoHU29noZztzutC1e9nkZxeKvV52gyO63htg7zIv7i57mu71G0qRvEOy1PwzmHbkdPaU5jbqCioXQ09eY0mhKeKnoa8921dy7kqVGMMU0MT1mfMZLMjtf3cDt3RMTylKbhaTh5IbeeRsAbIOQNaU7jMKdjJvcpSjkavdudlqfhJMJdD28dnxMxls6RzRsWdgUa799mXtj6jOFkFnJ1hqfA8pSm4WnUs1ihQ0+gRz2NwxwVDaWjcXIaXT53Fy7H05h2eCrQbVXlc0NJ0vlgzEpcL4xOXzR6bU9jOJEBY0+Yq0c0wvOmNXqqXi8PrPCg5jQOb1Q0lI5mJD1CT6AHr8frqn3EF8Er3und7dYzGxysmt0eP6RGGIpbE/wWNMXTcEQjC54GPY1piMZI2vK4etx6XKinMRfQnIbS0QynhpkXnOe6vYjQHeie3oUrOew+CW51aoWoksMcsD2NvqiLMrE1WGh/xoFYuqRmeR3rSIXnTSs8NZKxRKM34HKSI0z/3Csdj4qG0tEcSh9iXj0XcKwL1/TCUwch4jIJ7hCeZ3kaTQxP9YR8BHwe9sfS4wntejyg0LxpJcKH09axdXsamgg/rFHRUDqakfQI84P1XcCnLRrx/dBVZ/GuUK+V02hieEpE6I8G2T+WtsJMgSh46xiV5XgaDS6PPpoeJeqP4ve471NzGoc/KhpKR3MofYjeoPvwCDQhrh4fakA05hXDU90hH0GfuxxMLfq7S0TD7RBgh65+MIWGQ1Qj6ZGGzv1Ydmx6a38pHY2KhtLRDKeG2+tp5NKQHoGuvvqOC/XaifBMU4bbOkwUjXn1HewIX2xfQ32PZEZcl9l1WBBaAMCh1PTWvFI6FxUNpWNJ5pKk8qm6cxo9gZ5iPL5u4gesbaRO0bBDQQfG0sUEdjOYlqcRXWRtY3sb6ns4PVy3p7EwvBCAg6mDDfWpdD4qGkrH4gz5rGf0FFh3u8PpYQqmgVh+fL+1bSQ8lRphz0iSI3ubV7WuPxrkYCKDaUg0jrC2zt9UJ6Pp0fpFI2SJxlByqKE+lc5HRUPpWJwQR73hqYXhhRRMoTFvI2F7Go0kwgs5hkeGOapUNFKj8I03w1fPtnIllchl4I6L4aZT4eCLxd393UGMgULiYGM5DWg8PJUeqVuwHU9jKKWicbiioqF0LM6FZ36oTtGw73YPJhsIkTjhqXpzGna+IZQbY3FveHz/H/8LBtfAnnXw6JcqH//M92HLg3BwKzz078Xdi7qDgEFSw/WLRni+NemwgfBUvpBnJFN/ItzJaaincfiioqF0LPsTVlhlUWRRXcdN6253bI+1rdfTsNsvlBEWO56GMbDuTlh5Dpz4TnjmTijkyx//1O3QfwK89gPw3H3F2hwD8yNESOMpZOubcAjWpMPooobCU4fShyiYAn3h+sQz6o8S8ATU0ziMUdFQOpa9CesOuV7RcO52G0rGju6EYC+E6hs1RJdlY5+MsHie7WkMb7dCTSdcaD0SB2DnE1OPTRyEwbWw6iI4/u2QT8O23wOwdEGYBWIPH44srP/viS5qKDx1IGl5XP3h+sRTRFgYXqiJ8MMYFQ2lY9mf2M/84HwC3vqGsE4rGTuyE3qX1H+cPVKpX0Y4ap7taez4k7VddiYc+yYQD2z59dRjt/8eMJZHsuz14A3CS78FoDvk55iQvVhh95EN2HUkjO2u+zDHy6vX0wDr/Gt46vBFRUPpWPYl9tEfqTNMhDUr2SveBj2NQehpXDSWeEfpd4bc7viTNYt70YlWfuGIVfDyY1OPfel31qKHS04DfwgWv9ryPGyOjybsPo6o3655y+DQditUVgeOp9GIaCyKLGJPfE/dxymzAxUNpWPZl9xXd2gKwCMeFoQWFC98Dtl8lq898zW+9MSXist+T2FksDFPwx8mLl0cHUkgIta+HY9bQuCs0LvsdZYY5LMTj33pEcsb8dke1cBrYffTxXZHh638RkOiMX+FVVGwzGq3uUKObzz7DW5cc+OUGfTF8FQDor2kewm74rswdQqVMjtQ0VA6lp2xnSzuWtzQsUdFj2JXbNeEfV95+it85emv8N/r/5t/efRfph6USUBiCHoHGupziF4G/PZM9HQM9m6ApaePN1j2OsjGYc+z4/viQ7D/OVhx1vi+gdMgl4K96wFYHoiRN0IqUOfoKYD5y63toZemvHXTUzfx5Se/zG0bb+NTj35qwnv7EvvoDnQT9NY/UXFJdAnJXFKT4YcpKhpKRzKSHmEkPcLynuUNHT/QPcBgbHDC592x8Q4uPOZCPnLaR3h4x8P8YdcfJh40tNnaLjy27v7i6Ry78z0cIcPWjl1PgsnD0jPGGy17nbUtDVE5z5e9vsT411rbHWsAWOIfZYhent+XqNsu5jmisX3C7t2x3dy+4Xbedey7+PCpH+bhHQ/z7P5xMdsR28FAtDHxdI4bHBus0VKZjahoKDNKrpBjw4ENxdnfDttHrYvcsu5lDX3ukugSdsd3ky1YIZ77X7qfTCHD+054H+874X0s7lrMzU/fPDGEsv8Fa9v3yrr7e3bnCIOmj4U5O5bvJMGXnDbeqGcxLDjaCkc5vPyYlfhecur4vt6l0L3YCm8B/bk97DR9bNzVwCKM81dY26GtE3b/94b/BuCDr/4glx5/KV3+Lu7adFfx/Z1jOxnoblA07ON2xnZO2J/MJXl2/7Mkc8mGPlfpDFQ0lBkjkU1w2c8v45KfXcL5Pz6fNXvWFN/bNroNoHFPIzpAwRSKCdm7N9/N8QuO54SFJxDwBnj/Se9n3f51E72NA5tAPGTnL+eRwUdYu2et66VInt4xzLbCkYQSuyGbtESj75UQWTCx4cpzrdFSeXsV2O1/sITFVxIGErE8FFt4gmPb2ek5kmd2DLv++58/+DwPvfwQcY/AgmOsHInNodQhfrL5J7zjmHewOLqYLn8Xb1n+Fn718q9I5pLkC3kGY4Ms7V7qur9SBroH8ImPrcPjQvXSyEtceM+FvPf+9/KOu9/BC4deaOizlZlHRUOZEbKFLNf85ho2DG3go6s/yqLIIv7pN/9UHPG0cWgjYV+YZT2NeRorelcAsOXQFjYd3MRzB5/jXce+Cw6+BN95Fxfd/VGOxM8tT9407m0MrmVk0Qm894HL+eCvP8jfPvC3fPDXHySRLR8WSufTbDq4iZH0CL/fcoB4t9UnQ1th8E8T8xkOK8+xqvDtespKTu9+Bpa/fmq7pWfAyMtwaDsyMgjzV/LI5v0ks0k2HdxUOZEP3LbhNt5937v58MMf5sJ7LmTLka+EXU8X379r43dJ59Nc9tgd8PU3wEu/4x1Hv4N4Ns5vdvyGl8deJlfIsaJnRY2zXJ6gN8ix849lw9AGwPImr33kWtK5NJ953WcwGD7wyw/w8ujLDX2+MrN0lGiIyPkisklEtojItWXeD4rIXfb7j4vIihkwU3HJWGas7BLlxhiu+8N1/H7X7/nM6z7DZasu48Zzb2QsO8YX/vQFANbtX8cJC07A52msjP3xC47HJz6ePfAsP9n8E/weP39Ot3WR3PUk/uP/gg8cHGLdwY089uLPIZ8lsXMNH+zxsHV4K58/+/N8/LUf57Fdj/GhX39ognAYY/jBph/wxh+8kYvvu5jzfnAea8e+zZFHH281eO5eSB7CDLyWh15+iCsfvJL33PcePv/459lzxAlWm60PWXM2TJ7Y0edyy9O38N6fvZfLf3E5dz5/J9kBO6z1xLfBFJi37FXs9zzEOXedy8X3XcwbfvAGbn76ZrIlI7GMMdz05E3cuPZG3rL8LdzyplswxvB3ma1sS+yBQ9tJpMf4/rPf5KxEkmNWnAepEfjOO1m9/SmO6jqKH2/+MesPWAn4VX2rGjr3AKsWrmL9gfXkC3lu33g7G4c28skzP8nFr7iYb7z1GxRMgf/74P+dMsINLA90T3yP1uToUKRThsWJiBd4AXgLMAisAS41xmwsafNB4GRjzJUicglwkTHmr6t97urVq83atWurNVFsCqZAKpcilU8R8AQI+8J47eGixhj2JvYyODbI3sRe8iZPb6CXRZFFHNF1BPOD8ymYAs8fep5HBx/l0Z2Psu7AOgqmwKqFq7jo2It4+9FvJ+QLcf2frueuTXfxoVM+xJWvvrLY/389/V/c8swtfOqMT/Hvj/87V51yFVedfCVkE9ayGoUchBdYcxlKiQ/BgResRPaBzVZ1u/4T+Out3yUjsDexj7P8C7hhw6PWnIlL7oAFR5N98be8/eGrWCR+vnHS1Xxk7fU8FonwH2/4Em9e/mYAfvbiz/iXR/6FZV2rONn/j2zYNcKewB3EfU/yip5TuPykS/jWkw+yJflrjoos5YZt63l1fIQtfj/Xv+bt/HH/UwxEB1javZS1e9fi8/i4IhvkfcPD+Bccw30jm/j/+vs5mD7EaUecRjwb5/mDz3PcvGP5+JanOWPsIDt8Xj518tt48tB65nES1579v/j51of47a5fEiosZ2Hico5bsJyh0J08O/pLLjr2r/jM6/4Vr8fLtpFtXHb/+wgkhrht5aV8d//jfCf1Mrcv+0tOOe/frPP64/fDpvv52vFn85X0dk7pP4Wtw1v43amfxLdnvTWjPNgNR7wKFp9shbu8ZcTcGGvUl3j5xeBDfOy3H+Nfz/xXblhzA68/6vV8+bwvF4cjr9u/jvf/8v0s71nON9/2TSK+CA/veJgfvfAjHtv1GAZDxBfh3KXn8rblb+PPlvwZIZ/1f49n4wyODTI4Nkg8F6cv1MeR0SM5quuoYhvnO5vMJRnLjOH1eOkJ9NQ9UXSuIiJPGGNWl32vg0TjdcB1xpi32a8/AWCM+XxJmwfsNo+JiA/YA/SbKn9Eo6Lxv752Goc86fr+hrJ73Z3fgkAB65G3nwN4AY+xtuK8b7cx9qcbu73YbQXLhRS7bU6sRxbBCPgM+IzBi/U8J5ASIeWZ+hcEC4awMaQFkp7KjmmgYPBiim1OTGd4fSJNwBge7AqzOegnWDAEjWHU6+Gy4TH+8dAIAoh9jrLApUuOYHMggM8Y7h3cxdLc1LWakgSIESFFkPmMEmU8sZrBh2Dwk+e2nm5uXGgNU/3ezj1sz5zOZ80VJBm/sCzvvpvt/b8nWCiQ9njI7b6IQux1+DyC1yPkC4Z06ElCR90FxodHDIY8+aELSOw/i7DfRzKb59yTh9kduI3d8d0syuXY5/PRHejmQ6d8iL9+5V/j8/gYHBvk+jXX85sdvyFSKOA3hhGvl1f3v5pPnP4JVvWtwhjDQzse4oY/3cCu+C76czmGvD7CgS5Wd1/O//x+gAVdQQ7GM/i619N11N0UJAUmAJ4k6QPn4Rk+n75oiKDPgwGynkEyvTeQ9RTIivCaWB8vxv4VAI8IXvJcnr2Ltxd+xJ8PHEXS4+GisTifPTBEAWGMKBGS+MnZ59jPAVmAQQiQJWAyBEkTIlM8ryPi5y+WHsGw10M0b7hld4G+3PhvQYA1Yfi3RV4CBrwGYl6hP2d4UyzPorxhc0D4fcTLqFcIFAwL84aYRxjzlv+lAczLG0IFSHgg7oG8TGwbKBgiBsIF67eT9EDK/n041jm/C68BH9bWw/jvs2C39QBiv+f83pzeyv3qi5aYiW1Lt2bSY8pFZdKxk4+fsN/AvX/7FD5fHSWCnWNniWhcDJxvjHm//fp/A2cYY64uabPebjNov95qtzkw6bOuAK4AWLZs2Wnbt08cbuiGD9/6JsYK8UlGVnxRQRoqf7knt7Eu9GI/wGOs/QWBPIYCBiPWfg9SbC/2c+szxP5iG/tLZ/Ag+PDgRfAiiBHyYshjP8TgRQgYL0E8BIwXv/GQF0OaAmnJk5ECPjz0F8L0F0LMNwG8xkNMsgx7shzypBmWDDkKrCh088r8fHpMAGP/YA2wwxNjjW8vafK8Ot/HqkKf/d7En85BSfEr33aOLyzk5II1sS/jCZHxRDAiRHKjhPOjBPNxAoUkCd98hoOLORBcxlBoGcOBIxEMfant9Cc2sDb3MEcVQsyL/hXbuk8DKT1j1t3o2OgdJFJ/oK/nIqI955M3hnzekCtY/9XjjojS3b2Xp4Z/gd/r4+JXXMyy6DH87oX9PLxpPwPzw7z/7JVkC0l++MytvLD1Fxy94g1cfMqVZVfoXbtnDb94/EtkswnOPvUq3rjyrXhkoiCn82nu3nAHzz73IxYvPpWLT/t7FoWP4PtrXuaJ7Yc4cXEPb1t1JMFQjO8+910OpQ7x2v7zkNQreerlYQ7FM6RzBUSs9aDIriOb+m/CshgTvQaP1w/G+t8UjMEYWJLaTHfiR2z27ub1uVXsDp/OttAJZD0hPCbHkentLElv5aj0VnryBxFjyHkCZCVARoJkPSGyEkAoECok2M0+/hTYyxtT3SzPBUGk+P92fi8v+tI8GhzFAK/KdvHqTNT+BVjfiRyGF/xx1gdijEieLuNhQcFHfz5Af95HxMCoJ8+QJ8uQN8sBT5a0QNgIEeOlq+AhZCzxjHkKJCVPSgxJKdjfeyFoPPgYV42C8/uwf3u5kt9e6Q0ZjAuJwVCY9HMvfWlKrhBFQSh57bSxLvxCOSEYP85MOK7aZ976d4/i9dUf4p1zolGKhqcURVHqo5podFIifCdQOsZvwN5Xto0dnuoFdNqpoihKm+gk0VgDHCciK0UkAFwC3Dupzb3AZfbzi4GHquUzFEVRlObS2HjGFmCMyYnI1cADWLmobxljNojIZ4G1xph7gW8Ct4vIFuAglrAoiqIobaJjRAPAGHM/cP+kfZ8ueZ4C3t1uuxRFURSLTgpPKYqiKB2OioaiKIriGhUNRVEUxTUqGoqiKIprOmZyX6sQkf1A/VPCLfqAihMHZxC1qz7UrvpQu+rjcLRruTGmbK3fw140poOIrK00K3ImUbvqQ+2qD7WrPuaaXRqeUhRFUVyjoqEoiqK4RkWjOl+faQMqoHbVh9pVH2pXfcwpuzSnoSiKorhGPQ1FURTFNSoaiqIoimtUNAARebeIbBCRgoisnvTeJ0Rki4hsEpG3lew/3963RUSubYONd4nI0/Zjm4g8be9fISLJkve+2mpbyth2nYjsLLHh7SXvlT1/bbLriyLyvIisE5G7RWSevb8Tzllbvz8VbFgqIg+LyEb7+/9he3/F/2eb7dsmIs/aNqy19y0QkQdFZLO9nVoasbU2vbLkvDwtIqMi8o8zcc5E5Fsiss8uTufsK3t+xOIm+/u2TkRObbhjY8ycfwAnAK8EfgOsLtl/IvAMEARWAluxlm332s+PBgJ2mxPbaO9/AJ+2n68A1s/w+bsO+GiZ/WXPXxvteivgs59fD1zfCedspr8/JXYsBk61n3cDL9j/s7L/zxmwbxvQN2nfDcC19vNrnf/pDP4f9wDLZ+KcAecAp5Z+lyudH+DtwM+xqseeCTzeaL/qaQDGmOeMMZvKvPVO4E5jTNoY8xKwBTjdfmwxxrxojMkAd9ptW46ICPAe4Pvt6G+aVDp/bcEY80tjTM5++UesapCdwIx9f0oxxuw2xjxpPx8DngOWtNuOOnkncJv9/DbgXTNnCm8CthpjGl1xYloYY36HVVeolErn553Ad4zFH4F5IrK4kX5VNKqzBNhR8nrQ3ldpfzs4G9hrjNlcsm+liDwlIr8VkbPbZMdkrrbd3m+VhAxm8jxN5v9g3Wk5zOQ566TzAlghO+A1wOP2rnL/z3ZjgF+KyBMicoW97whjzG77+R7giJkxDbCKwJXevHXCOat0fpr2nZszoiEivxKR9WUebb/Dq4RLGy9l4hd1N7DMGPMa4BrgeyLS02bb/gs4BjjFtuc/mt1/g3Y5bT4J5IDv2rvacs5mCyISBX4M/KMxZpQZ/H9O4ixjzKnABcCHROSc0jeNFXeZkTkDYpWkvhD4ob2rU85ZkVadn46q3NdKjDFvbuCwncDSktcD9j6q7G+YWjaKiA/4S+C0kmPSQNp+/oSIbAVeAaydrj312FZi463A/9gvq52/ttglIpcDfwG8yf4Rte2cVaHl58UtIuLHEozvGmN+AmCM2Vvyfun/s60YY3ba230icjdWWG+viCw2xuy2wyv7ZsI2LCF70jlXnXLOqHx+mvadmzOeRoPcC1wiIkERWQkcB/wJWAMcJyIr7TuOS+y2rebNwPPGmEFnh4j0i4jXfn60beOLbbClyKTY6EWAM5qj0vlrl13nA/8MXGiMSZTsn+lzNlPfnwnY+bFvAs8ZY75Usr/S/7OdtnWJSLfzHGtQw3qs83SZ3ewy4Kftts1mgsffCefMptL5uRf4G3sU1ZnASEkYqz7aPeKgEx9Y/+RBrLvPvcADJe99EmukyybggpL9b8cabbIV+GSb7Pw2cOWkfX8FbACeBp4E3jED5+924Flgnf3lXFzr/LXJri1Ycdyn7cdXO+ictf37U8aGs7DCF+tKztHbq/0/22jb0Vijyp6x/1eftPcvBH4NbAZ+BSyYAdu6gCGgt2Rf288ZlmjtBrL29evvKp0frFFTN9vft2cpGSVa70OXEVEURVFco+EpRVEUxTUqGoqiKIprVDQURVEU16hoKIqiKK5R0VAURVFco6KhKIqiuEZFQ1EURXGNioaitBER6RMRIyIfEZE1IpISkRdE5K0zbZuiuEFFQ1Hayyn29v3Ax4GTsWYRf09EwjNllKK4RUVDUdrLKUAeuMgY85Ax5gUs8VgIHD+ThimKG1Q0FKW9nALcZ4uFw+gM2aIodaOioSjt5RTgqUn7Xg+ksBZ1VJSORkVDUdqEiISwatFP/t39E1ZZ3MTUoxSls5gzRZgUpQN4FdYS1ZeKyK+xCuR8CjgWq+67onQ86mkoSvs4BavOwWewaiE8BcwHzjbG7JlBuxTFNVpPQ1HahIh8BVhkjFGvQpm1qKehKO3jFKw5GYoya1HRUJQ2YNfjdibyKcqsRcNTiqIoimvU01AURVFco6KhKIqiuEZFQ1EURXGNioaiKIriGhUNRVEUxTUqGoqiKIprVDQURVEU1/z/x1sBTNvmD+8AAAAASUVORK5CYII=\n",
53 | "text/plain": [
54 | ""
55 | ]
56 | },
57 | "metadata": {
58 | "needs_background": "light"
59 | },
60 | "output_type": "display_data"
61 | }
62 | ],
63 | "source": [
64 | "hbar=1\n",
65 | "def delta_x_p(x0,p):\n",
66 | " delta_x_p=(1/np.sqrt(2*np.pi*hbar)) * cmath.exp(-1j*x0*p/hbar)\n",
67 | " return delta_x_p\n",
68 | " \n",
69 | "A=100.0; dp=0.05; Np=int( (2*A)/dx + 1)\n",
70 | "\n",
71 | "p=np.linspace(-A, A, Np)\n",
72 | "phi_p1=np.zeros(Np,dtype='complex')\n",
73 | "phi_p4=np.zeros(Np,dtype='complex')\n",
74 | "phi_p10=np.zeros(Np,dtype='complex')\n",
75 | "\n",
76 | "for i in range(Np):\n",
77 | " phi_p1[i]=0\n",
78 | " phi_p4[i]=0\n",
79 | " phi_p10[i]=0\n",
80 | " for k in range(N):\n",
81 | " phi_p1[i]=phi_p1[i] + dx * psi_1[k] * delta_x_p(x[k],p[i])\n",
82 | " phi_p4[i]=phi_p4[i] + dx * psi_4[k] * delta_x_p(x[k],p[i])\n",
83 | " phi_p10[i]=phi_p10[i] + dx * psi_10[k] * delta_x_p(x[k],p[i])\n",
84 | "\n",
85 | "plt.plot(p,np.abs(phi_p1)**2)\n",
86 | "plt.plot(p,np.abs(phi_p4)**2)\n",
87 | "plt.plot(p,np.abs(phi_p10)**2)\n",
88 | "\n",
89 | "plt.xlabel(\"$p$\", fontsize=14)\n",
90 | "plt.ylabel(\"$|\\phi(p)|^2$\", fontsize=14)\n",
91 | "plt.legend(['n=1','n=4','n=10'])\n",
92 | "plt.savefig('phi_p.png') \n",
93 | "plt.show()"
94 | ]
95 | },
96 | {
97 | "cell_type": "code",
98 | "execution_count": null,
99 | "id": "e7454748",
100 | "metadata": {},
101 | "outputs": [],
102 | "source": []
103 | },
104 | {
105 | "cell_type": "code",
106 | "execution_count": null,
107 | "id": "6da54bf7",
108 | "metadata": {},
109 | "outputs": [],
110 | "source": []
111 | }
112 | ],
113 | "metadata": {
114 | "kernelspec": {
115 | "display_name": "Python 3",
116 | "language": "python",
117 | "name": "python3"
118 | },
119 | "language_info": {
120 | "codemirror_mode": {
121 | "name": "ipython",
122 | "version": 3
123 | },
124 | "file_extension": ".py",
125 | "mimetype": "text/x-python",
126 | "name": "python",
127 | "nbconvert_exporter": "python",
128 | "pygments_lexer": "ipython3",
129 | "version": "3.9.4"
130 | }
131 | },
132 | "nbformat": 4,
133 | "nbformat_minor": 5
134 | }
135 |
--------------------------------------------------------------------------------
/notebooks/NumQM_Basic_04.ipynb:
--------------------------------------------------------------------------------
1 | {
2 | "cells": [
3 | {
4 | "cell_type": "code",
5 | "execution_count": 1,
6 | "id": "0ff81497",
7 | "metadata": {},
8 | "outputs": [],
9 | "source": [
10 | "import numpy as np\n",
11 | "from numpy import linalg as npla\n",
12 | "import matplotlib.pyplot as plt\n",
13 | "from scipy import integrate"
14 | ]
15 | },
16 | {
17 | "cell_type": "code",
18 | "execution_count": 2,
19 | "id": "42aff115",
20 | "metadata": {},
21 | "outputs": [],
22 | "source": [
23 | "def eigen(A):\n",
24 | " eigenValues, eigenVectors = npla.eig(A)\n",
25 | " idx = np.argsort(eigenValues)\n",
26 | " eigenValues = eigenValues[idx]\n",
27 | " eigenVectors = eigenVectors[:,idx]\n",
28 | " return (eigenValues, eigenVectors)"
29 | ]
30 | },
31 | {
32 | "cell_type": "code",
33 | "execution_count": 3,
34 | "id": "5c61bb9f",
35 | "metadata": {},
36 | "outputs": [],
37 | "source": [
38 | "L=10.0 # box length is 2L; [-L,L]\n",
39 | "k=1 # force constant\n",
40 | "m=1 # particle mass \n",
41 | "hbar=1 # 1 in atomic units"
42 | ]
43 | },
44 | {
45 | "cell_type": "code",
46 | "execution_count": 4,
47 | "id": "ff743881",
48 | "metadata": {},
49 | "outputs": [
50 | {
51 | "name": "stdout",
52 | "output_type": "stream",
53 | "text": [
54 | "Number of basis: 1 , ground state energy is: 6.546885307943112\n",
55 | "Number of basis: 2 , ground state energy is: 6.546885307943112\n",
56 | "Number of basis: 4 , ground state energy is: 2.2409822186260655\n",
57 | "Number of basis: 8 , ground state energy is: 0.7712925817042399\n",
58 | "Number of basis: 16 , ground state energy is: 0.5026588346751345\n",
59 | "Number of basis: 32 , ground state energy is: 0.49999999991960487\n"
60 | ]
61 | }
62 | ],
63 | "source": [
64 | "def fn_V(x):\n",
65 | " psi_i=np.sqrt(1/L)*np.sin((i+1)*(x-L)*np.pi/(2*L))\n",
66 | " psi_j=np.sqrt(1/L)*np.sin((j+1)*(x-L)*np.pi/(2*L))\n",
67 | " fn_V=psi_i * k * x**2/2 * psi_j\n",
68 | " return fn_V\n",
69 | "\n",
70 | "for iN in range(0,6):\n",
71 | " \n",
72 | " N=2**iN # No. of basis functions\n",
73 | "\n",
74 | " V=np.zeros([N,N])\n",
75 | " T=np.zeros([N,N])\n",
76 | " H=np.zeros([N,N])\n",
77 | " \n",
78 | " for i in range(N):\n",
79 | " for j in range(N):\n",
80 | " Int_V=integrate.quadrature(fn_V, -L, L,maxiter=1000)\n",
81 | " V[i][j]=Int_V[0]\n",
82 | " #kinetic energy part is same as in the particle-in-a-box \n",
83 | " T[i][i]=(i+1)**2 * hbar**2 * np.pi**2 / (8 * m * L**2)\n",
84 | "\n",
85 | " H=T+V\n",
86 | "\n",
87 | " E,V=eigen(H)\n",
88 | "\n",
89 | " print(\"Number of basis: \", N, \", ground state energy is:\", E[0])"
90 | ]
91 | },
92 | {
93 | "cell_type": "code",
94 | "execution_count": 5,
95 | "id": "643f3578",
96 | "metadata": {},
97 | "outputs": [
98 | {
99 | "name": "stdout",
100 | "output_type": "stream",
101 | "text": [
102 | "0 0.49999999991960487\n",
103 | "1 1.500000003533623\n",
104 | "2 2.5000000246525915\n",
105 | "3 3.5000000749476574\n",
106 | "4 4.500003826380895\n",
107 | "5 5.500009108730652\n",
108 | "6 6.500213561983046\n",
109 | "7 7.500380483848162\n",
110 | "8 8.50489994173305\n",
111 | "9 9.507109605274334\n",
112 | "10 10.550503775703861\n",
113 | "11 11.563037889597\n",
114 | "12 12.757188589561512\n",
115 | "13 13.790161054294524\n",
116 | "14 15.274948394336956\n",
117 | "15 16.323820558552228\n",
118 | "16 18.175821285164076\n",
119 | "17 19.22309685760712\n",
120 | "18 21.47078218078809\n",
121 | "19 22.495304266567338\n",
122 | "20 25.155539320689343\n",
123 | "21 26.135710969665308\n",
124 | "22 29.225350687266882\n",
125 | "23 30.13958386030048\n",
126 | "24 33.67696348822975\n",
127 | "25 34.50365514827044\n",
128 | "26 38.50946635546445\n",
129 | "27 39.22763463005119\n",
130 | "28 43.745025808894155\n",
131 | "29 44.34804530869218\n",
132 | "30 50.588924425384036\n",
133 | "31 51.22056108474399\n"
134 | ]
135 | }
136 | ],
137 | "source": [
138 | "for i in range(N):\n",
139 | " print(i,E[i])"
140 | ]
141 | },
142 | {
143 | "cell_type": "code",
144 | "execution_count": 8,
145 | "id": "b3a04f81",
146 | "metadata": {},
147 | "outputs": [
148 | {
149 | "data": {
150 | "image/png": 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\n",
151 | "text/plain": [
152 | ""
153 | ]
154 | },
155 | "metadata": {
156 | "needs_background": "light"
157 | },
158 | "output_type": "display_data"
159 | }
160 | ],
161 | "source": [
162 | "x=np.linspace(-L, L, 101)\n",
163 | "Vharm=k*x**2/2\n",
164 | "\n",
165 | "psi0=np.zeros(101)\n",
166 | "psi1=np.zeros(101)\n",
167 | "psi2=np.zeros(101)\n",
168 | "psi3=np.zeros(101)\n",
169 | "psi4=np.zeros(101)\n",
170 | "for i in range(N):\n",
171 | " psi0=psi0+V[i][0]*np.sqrt(1/L)*np.sin((i+1)*(x-L)*np.pi/(2*L))\n",
172 | " psi1=psi1+V[i][1]*np.sqrt(1/L)*np.sin((i+1)*(x-L)*np.pi/(2*L))\n",
173 | " psi2=psi2+V[i][2]*np.sqrt(1/L)*np.sin((i+1)*(x-L)*np.pi/(2*L))\n",
174 | " psi3=psi3+V[i][3]*np.sqrt(1/L)*np.sin((i+1)*(x-L)*np.pi/(2*L))\n",
175 | " psi4=psi4+V[i][4]*np.sqrt(1/L)*np.sin((i+1)*(x-L)*np.pi/(2*L))\n",
176 | " \n",
177 | "plt.plot(x,np.abs(psi0)**2+E[0])\n",
178 | "plt.plot(x,np.abs(psi1)**2+E[1])\n",
179 | "plt.plot(x,np.abs(psi2)**2+E[2])\n",
180 | "plt.plot(x,np.abs(psi3)**2+E[3])\n",
181 | "plt.plot(x,np.abs(psi4)**2+E[4])\n",
182 | "plt.plot(x,Vharm)\n",
183 | "plt.xlabel(\"$x$\", fontsize=14)\n",
184 | "plt.ylabel(\"$|\\psi(x)|^2$\", fontsize=14)\n",
185 | "plt.savefig('psi_harm.png') \n",
186 | "plt.legend(['n = 0','n = 1','n = 2','n = 3','n = 4'])\n",
187 | "plt.xlim(-10,10)\n",
188 | "plt.ylim(0,10)\n",
189 | "plt.show()"
190 | ]
191 | },
192 | {
193 | "cell_type": "code",
194 | "execution_count": null,
195 | "id": "b45d26db",
196 | "metadata": {},
197 | "outputs": [],
198 | "source": []
199 | }
200 | ],
201 | "metadata": {
202 | "kernelspec": {
203 | "display_name": "Python 3",
204 | "language": "python",
205 | "name": "python3"
206 | },
207 | "language_info": {
208 | "codemirror_mode": {
209 | "name": "ipython",
210 | "version": 3
211 | },
212 | "file_extension": ".py",
213 | "mimetype": "text/x-python",
214 | "name": "python",
215 | "nbconvert_exporter": "python",
216 | "pygments_lexer": "ipython3",
217 | "version": "3.9.4"
218 | }
219 | },
220 | "nbformat": 4,
221 | "nbformat_minor": 5
222 | }
223 |
--------------------------------------------------------------------------------
/notebooks/NumQM_Basic_05.ipynb:
--------------------------------------------------------------------------------
1 | {
2 | "cells": [
3 | {
4 | "cell_type": "code",
5 | "execution_count": 1,
6 | "id": "81e46ad0",
7 | "metadata": {},
8 | "outputs": [],
9 | "source": [
10 | "import numpy as np\n",
11 | "from numpy import linalg as npla\n",
12 | "import matplotlib.pyplot as plt\n",
13 | "from scipy import integrate"
14 | ]
15 | },
16 | {
17 | "cell_type": "code",
18 | "execution_count": 2,
19 | "id": "b1029606",
20 | "metadata": {},
21 | "outputs": [],
22 | "source": [
23 | "def eigen(A):\n",
24 | " eigenValues, eigenVectors = npla.eig(A)\n",
25 | " idx = np.argsort(eigenValues)\n",
26 | " eigenValues = eigenValues[idx]\n",
27 | " eigenVectors = eigenVectors[:,idx]\n",
28 | " return (eigenValues, eigenVectors)"
29 | ]
30 | },
31 | {
32 | "cell_type": "code",
33 | "execution_count": 3,
34 | "id": "7c6a13d2",
35 | "metadata": {},
36 | "outputs": [],
37 | "source": [
38 | "L=15.0 # box length is 2L; [-L,L]\n",
39 | "m=1 # particle mass \n",
40 | "hbar=1 # 1 in atomic units"
41 | ]
42 | },
43 | {
44 | "cell_type": "code",
45 | "execution_count": 10,
46 | "id": "a8b1af48",
47 | "metadata": {},
48 | "outputs": [
49 | {
50 | "name": "stdout",
51 | "output_type": "stream",
52 | "text": [
53 | "Number of basis: 1 , ground state energy is: -3.0563258068171444\n",
54 | "Number of basis: 2 , ground state energy is: -3.156640541974056\n",
55 | "Number of basis: 4 , ground state energy is: -3.924186324234983\n",
56 | "Number of basis: 8 , ground state energy is: -4.547315446207627\n",
57 | "Number of basis: 16 , ground state energy is: -5.2692879329887035\n",
58 | "Number of basis: 32 , ground state energy is: -5.486268540734763\n"
59 | ]
60 | }
61 | ],
62 | "source": [
63 | "def potential(x): # 1-D molecule\n",
64 | " potential = -6/np.sqrt((x+4)**2+1)-4/np.sqrt((x-4)**2+1)\n",
65 | " return potential\n",
66 | " \n",
67 | "def fn_V(x):\n",
68 | " psi_i=np.sqrt(1/L)*np.sin((i+1)*(x-L)*np.pi/(2*L))\n",
69 | " psi_j=np.sqrt(1/L)*np.sin((j+1)*(x-L)*np.pi/(2*L))\n",
70 | " Nx=x.size\n",
71 | " pot=np.zeros(Nx)\n",
72 | " for ix in range(Nx):\n",
73 | " pot[ix]=potential(x[ix])\n",
74 | " \n",
75 | " fn_V=psi_i * pot * psi_j\n",
76 | " return fn_V\n",
77 | "\n",
78 | "for iN in range(0,6):\n",
79 | " \n",
80 | " N=2**iN # No. of basis functions\n",
81 | "\n",
82 | " V=np.zeros([N,N])\n",
83 | " T=np.zeros([N,N])\n",
84 | " H=np.zeros([N,N])\n",
85 | " \n",
86 | " for i in range(N):\n",
87 | " for j in range(N):\n",
88 | " Int_V=integrate.quadrature(fn_V, -L, L,maxiter=1000)\n",
89 | " V[i][j]=Int_V[0] \n",
90 | " T[i][i]=(i+1)**2 * hbar**2 * np.pi**2 / (8 * m * L**2)\n",
91 | "\n",
92 | " H=T+V\n",
93 | "\n",
94 | " E,V=eigen(H)\n",
95 | "\n",
96 | " print(\"Number of basis: \", N, \", ground state energy is:\", E[0])"
97 | ]
98 | },
99 | {
100 | "cell_type": "code",
101 | "execution_count": 14,
102 | "id": "6d28b625",
103 | "metadata": {},
104 | "outputs": [
105 | {
106 | "data": {
107 | "image/png": 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\n",
108 | "text/plain": [
109 | ""
110 | ]
111 | },
112 | "metadata": {
113 | "needs_background": "light"
114 | },
115 | "output_type": "display_data"
116 | }
117 | ],
118 | "source": [
119 | "x=np.linspace(-L, L, 101)\n",
120 | "Vharm=np.zeros(101)\n",
121 | "for ix in range(101):\n",
122 | " Vharm[ix]=potential(x[ix])\n",
123 | "\n",
124 | "for k in range(16): \n",
125 | " psi0=np.zeros(101)\n",
126 | " for i in range(N):\n",
127 | " psi0=psi0+V[i][k]*np.sqrt(1/L)*np.sin((i+1)*(x-L)*np.pi/(2*L))\n",
128 | " \n",
129 | " plt.plot(x,np.abs(psi0)**2+E[k])\n",
130 | "\n",
131 | "\n",
132 | "plt.plot(x,Vharm)\n",
133 | "plt.xlabel(\"$x$\", fontsize=14)\n",
134 | "plt.ylabel(\"$|\\psi(x)|^2$\", fontsize=14)\n",
135 | "plt.savefig('psi_1Dmol.png') \n",
136 | "#plt.legend(['n = 0','n = 1','n = 2','n = 3','n = 4'])\n",
137 | "plt.xlim(-L,L)\n",
138 | "#plt.ylim(-10,10)\n",
139 | "plt.show()"
140 | ]
141 | },
142 | {
143 | "cell_type": "code",
144 | "execution_count": null,
145 | "id": "0f14e098",
146 | "metadata": {},
147 | "outputs": [],
148 | "source": []
149 | }
150 | ],
151 | "metadata": {
152 | "kernelspec": {
153 | "display_name": "Python 3",
154 | "language": "python",
155 | "name": "python3"
156 | },
157 | "language_info": {
158 | "codemirror_mode": {
159 | "name": "ipython",
160 | "version": 3
161 | },
162 | "file_extension": ".py",
163 | "mimetype": "text/x-python",
164 | "name": "python",
165 | "nbconvert_exporter": "python",
166 | "pygments_lexer": "ipython3",
167 | "version": "3.9.4"
168 | }
169 | },
170 | "nbformat": 4,
171 | "nbformat_minor": 5
172 | }
173 |
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/pdf/NIUS30Dec2021_NumQM.pdf:
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https://raw.githubusercontent.com/raghurama123/NumQM_Basic/59286ff3c7339f3c8055ff60200e04f021b187aa/pdf/NIUS30Dec2021_NumQM.pdf
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