{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 径向本征求解器\n", "\n", "[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/bud-primordium/AtomSCF/blob/main/docs/source/tutorials/02-solver.ipynb)\n", "\n", "## 学习目标\n", "\n", "- 理解径向薛定谔方程的数值求解方法\n", "- 对比不同求解器(FD2/FD5)的精度差异\n", "- 验证氢原子解析解并分析数值误差\n", "\n", "## 径向薛定谔方程\n", "\n", "球对称势下的径向方程:\n", "\n", "$$\\left[-\\frac{1}{2}\\frac{d^2}{dr^2} + \\frac{l(l+1)}{2r^2} + V(r)\\right] u(r) = E u(r)$$\n", "\n", "其中 $u(r) = r R(r)$ 是径向约化波函数,边界条件:$u(0) = 0$,$u(\\infty) = 0$。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 理论基础:有限差分法\n", "\n", "径向薛定谔方程:\n", "\n", "$$\\left[-\\frac{1}{2}\\frac{d^2}{dr^2} + \\frac{l(l+1)}{2r^2} + V(r)\\right]u(r) = Eu(r)$$\n", "\n", "### 五点中心差分(O(h⁴) 精度)\n", "\n", "二阶导数离散化:\n", "\n", "$$\\frac{d^2u}{dr^2}\\bigg|_i \\approx \\frac{-u_{i-2}+16u_{i-1}-30u_i+16u_{i+1}-u_{i+2}}{12h^2}$$\n", "\n", "构造 Hamiltonian 矩阵 $H$,求解广义本征值问题:\n", "\n", "$$H\\mathbf{u} = E\\mathbf{u}$$\n", "\n", "**算法实现**:\n", "1. 构造五对角矩阵 `H`\n", "2. 调用 `scipy.linalg.eigh()` 求解\n", "3. 提取束缚态($E < 0$)并归一化\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "execution": { "iopub.execute_input": "2025-12-04T04:12:58.224953Z", "iopub.status.busy": "2025-12-04T04:12:58.224686Z", "iopub.status.idle": "2025-12-04T04:12:58.229916Z", "shell.execute_reply": "2025-12-04T04:12:58.229824Z" } }, "outputs": [], "source": [ "# 环境配置\n", "import sys\n", "\n", "if \"google.colab\" in sys.modules:\n", " !pip install -q git+https://github.com/bud-primordium/AtomSCF.git" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2025-12-04T04:12:58.235993Z", "iopub.status.busy": "2025-12-04T04:12:58.235891Z", "iopub.status.idle": "2025-12-04T04:13:16.412249Z", "shell.execute_reply": "2025-12-04T04:13:16.412063Z" } }, "outputs": [], "source": [ "# 配置中文字体(避免乱码)\n", "import matplotlib.pyplot as plt\n", "import matplotlib\n", "\n", "# 跨平台中文字体配置\n", "matplotlib.rcParams['font.sans-serif'] = [\n", " 'Arial Unicode MS', # macOS\n", " 'WenQuanYi Micro Hei', # Linux\n", " 'SimHei', # Windows\n", " 'DejaVu Sans' # Fallback\n", "]\n", "matplotlib.rcParams['axes.unicode_minus'] = False\n", "\n", "# 清除字体缓存(重要!)\n", "try:\n", " import matplotlib.font_manager as fm\n", " fm._load_fontmanager(try_read_cache=False)\n", "except Exception:\n", " pass\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "execution": { "iopub.execute_input": "2025-12-04T04:13:16.417627Z", "iopub.status.busy": "2025-12-04T04:13:16.417502Z", "iopub.status.idle": "2025-12-04T04:13:16.586008Z", "shell.execute_reply": "2025-12-04T04:13:16.585888Z" } }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from atomscf.grid import radial_grid_linear\n", "from atomscf.operator import solve_bound_states_fd, solve_bound_states_fd5\n", "\n", "plt.rcParams[\"figure.figsize\"] = (12, 5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 氢原子势函数\n", "\n", "类氢离子的库仑势:$V(r) = -Z/r$" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "execution": { "iopub.execute_input": "2025-12-04T04:13:16.590840Z", "iopub.status.busy": "2025-12-04T04:13:16.590737Z", "iopub.status.idle": "2025-12-04T04:13:16.862316Z", "shell.execute_reply": "2025-12-04T04:13:16.861877Z" } }, "outputs": [ { "data": { "image/png": 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7d2+FhIQoIiJCTz/9tC5cuOCw7ZtvvqnGjRuratWqatWqlVNT4wIAAABAWfHIkNWvXz/5+fnp2LFj2r59u1auXKlJkyYVajd37ly99tpr+vLLL5WamqqXX35ZAwcO1KZNm0yoGgAAAAA8MGTt27dPq1at0vTp0xUSEqK6detqzJgxSkhIKNQ2KSlJcXFxatWqlSwWi3r27KnmzZtr3bp1JlQOAAAAAB44hXtiYqKqV6+uqKgo+7bY2FgdPXpUKSkpBW54OXbs2AL77t27V7t379b111/v8NhZWVnKysqyr1utVp0+fVrh4eGFpsAFAAAAUHHYbDalp6erTp06VzyTq8eFrPT0dAUFBRXYlreekZFRIGRdbM+ePbrzzjv10EMPqWPHjg7bTJ06VRMnTnRpvQAAAAC8x+HDhwsM+JSGx4WskJAQnT17tsC2vPWQkBCH+3z33Xd64IEH1K9fP7399ttFHnvs2LEFbnyZmpqqevXq6cCBA0WGN8AVrFarTp06pYiICO5xgzJFX4O70NfgLvQ1uEtKSoquuuqqIjNHSXhcyGrZsqVOnz6to0ePqm7dupKkHTt2KCoqStWqVSvU/rXXXtOLL76ot956S0OHDi322AEBAQoICCi0PTQ0lJCFMmW1WpWdna3Q0FB+QaBM0dfgLvQ1uAt9De7misuIPK6nNm7cWB06dNCYMWOUmZmpAwcOaMqUKQ4D1Jw5czRx4kStXLnysgELAAAAANzB40KWJH3yySdKSUlRjRo1dN1116lHjx4aN26cJCk4OFjz58+XJE2cOFGZmZnq0qWLgoOD7Y/4+HgzywcAAABQgXnc6YKSVKdOHX3zzTcOX8vIyLAvHzlyxF0lAQAAAIBTPHIkCwAAAADKK0IWAAAAALgQIQsAAAAAXIiQBQAAAAAuRMgCAAAAABciZAEAAACACxGyAAAAAMCFCFkAAAAA4EKELAAAAABwIUIWAAAAALgQIQsAAAAAXIiQBQAAAAAuRMgCAAAAABciZAEAAACACxGyAAAAAMCFCFkAAAAA4EKELAAAAABwIUIWAAAAALgQIQsAAAAAXIiQBQAAAAAuRMgCAAAAABciZAEAAACACxGyAAAAAMCFCFkAAAAA4EKELAAAAABwIUIWAAAAALgQIQsAAAAAXIiQBQAAAAAuRMgCAAAAABciZAEAAACACxGyAAAAAMCFCFkAAAAA4EKELAAAAABwIUIWAAAAALgQIQsAAAAAXMgjQ1ZSUpJ69+6tkJAQRURE6Omnn9aFCxcctl26dKlatmypwMBANWvWTF999ZWbqwUAAACAfB4Zsvr16yc/Pz8dO3ZM27dv18qVKzVp0qRC7fbu3as+ffroxRdfVHp6uqZOnaoHHnhAv/32mwlVAwAAAIDkZ3YBl9q3b59WrVqlw4cPKyQkRCEhIRozZozGjBmjyZMnF2j7wQcfqH379nrggQckSffee686dOigjz76SFOmTHH6PXNzc5Wbm1tou8VikY+PT4F2xfH19a0Qba1Wq2w2m0e39fHxkcVi8ai2ef3M0T6lPa7NZpPVai2y7cV92JvbSsX3YU9oK7nvZ7m4vsZnhMETPyPKom1Z/nwW19f4jCh5W8nzft97ymdEcX2Nz4gra+sJP5+e0FYqOg+UlseFrMTERFWvXl1RUVH2bbGxsTp69KhSUlIUGhpaoG1sbGyB/WNjY7Vz506Hx87KylJWVpZ9PS0tTZK0fPlyBQUFFWpfo0YN3XDDDfb1pUuXFvnNDw8P180332xf/+6775Sdne2wbWhoqDp27GhfX7FihTIzMx22DQkJUadOnezrP/74o9LT0x22rVKlirp06WJfX7dunVJSUhy2rVSpkrp162ZfX79+vZKTkx229fX1VY8ePezrGzduVFJSksO2knTXXXfZl7ds2aLjx48X2bZHjx72D71t27bp8OHDRbbt1q2bKlWqJMn4tz948GCRbTt37qzAwEBJ0u7du7Vv374i23bq1EkhISGSpD179uj3338vsm3Hjh3tfXDfvn3avXt3kW1vvvlmhYeHS5IOHjyo//73v6pWrZr9g+1i7dq1U82aNSVJhw8f1rZt24o8btu2bVWnTh1J0rFjx/Tzzz8X2bZNmzaKjo6WJJ04cUKbNm0qsm3r1q0VExMjSUpOTtZPP/1UZNsWLVqoYcOGkqSUlBStXbu2yLZNmjRR06ZNJUnp6elavXp1kW0bNmyoFi1aSJLOnTunFStWFNk2JiZGrVu3liRlZ2dr+fLlRbaNjo5WmzZtJBkfokuWLCmybe3atXXdddfZ17/99tsi23riZ8SaNWt05MgRh32Nz4h8nvgZkZiYWGRbT/yM+O9//6vU1FSHfY3PCIMnfkaUx78jjh07VmRf4zPC4ImfEeXx74izZ88W2b6kPC5kpaenFwo8eesZGRkFQlZRbTMyMhwee+rUqZo4cWKh7ampqcrJySm03d/fv8CHQGpqapEfjj4+PgXapqSkFHkdmc1mK9T2/PnzDtvm5uYWalvU15eVlVWg7ZkzZ+xB8lKXfm1nzpxRamqqw7a+vr5Ot5VUoO3p06cv2zbvw9GZtnkfjs60zftwTE5OLrbtyZMn7b+cnGmb90vPmbZ5/SU5OVlnz56VzWYr8L8meU6dOmX/xXHq1Klij3vq1Cn5+fk53TYgIMCptsnJyfbv2eW+v8nJyfZfKKmpqZdtm9cnMjIynG577ty5YtuePn3a3jY7O7vYtkFBQfa2ubm5xbYNCAgo9HNfFE/8jDhz5kyRfY3PiIJtPe0z4nI/y572GZGSkqJz58457Gt8Rhg88TOiPP4dUVxf4zPC4ImfEeXx7whXhiyLrbjxRBMsWrRIQ4YMKfC/ITt27NDVV1+tlJQUVatWzb69V69eatiwoV5//XX7tlGjRunAgQP68ssvCx3b0UhWdHS0kpKSCoS3PAzzO27LqUAlb5uTk6OkpCRFRkY6DFkM819ZW4lTgfJcuHBBJ0+eLLKv8Rlh8LTPiPJ4KlBOTk6RfY3PiJK3lTzv972nfEbk5uYW2df4jLiytp7w8+kJbSWjD6ekpKhGjRpKTU1V1apVi9zXGR43ktWyZUudPn1aR48eVd26dSUZISsqKqpAwMpru3nz5gLbduzYoZtuusnhsQMCAuxp/GL+/v7y9/e/bG2O/mChLW2d4efnJz8/P/n7+192v5IcVyr4S6Mit/WEf2dPaOvv718mfY225bOtVHY/cxaLxem+xmcEba+krY+Pj1N9zVPqLU9tJc/4+fSEtj4+Pk7lAaeP57IjuUjjxo3VoUMHjRkzRpmZmTpw4ICmTJmioUOHFmrbv39/rVmzRl9//bVyc3O1YMECrVu3Tv379zehcgAAAADwwJAlSZ988ol9uO66665Tjx49NG7cOElScHCw5s+fL0lq1qyZFixYoOeff17BwcGaNGmSvvjiCzVp0sTM8gEAAABUYB53uqAk1alTR998843D1y69WLNXr17q1auXG6oCAAAAgMvzyJEsAAAAACivCFkAAAAA4EKELAAAAABwIUIWAAAAALgQIQsAAAAAXIiQBQAAAAAuRMgCAAAAABciZAEAAACACxGyAAAAAMCFCFkAAAAA4EKELAAAAABwIUIWAAAAALgQIQsAAAAAXIiQBQAAAAAuRMgCAAAAABfyM7sAAAAAAHBWTo50/ryUmWk8X/y4dNvF61lZRS83bCg984zraiRkAQAAAHCazZYfdC4XbEoThi63T26u67+mG28kZAEAAAC4yIUL0rlzRhC53LOzbfIejoKO1Wr2V+xaWVmuPR4hCwAAACgDecEn71HSoFOStmUxumMmi0WqUkWqXDn/UdL1vG0BAfnPedsvXQ4Odm39hCwAAABUSLm5Rkg5e9Z4XLzsaL2kbS5cMPsrvDI+Ps4HmdKEn+LW/f2NoOVOKSmuOxYhCwAAAB4rN1dKT7fYR4UyMvIfVxqOzp83+6srOV9fKTDQeFSpkv988bKrXjMj6HgLQhYAAABcwmo1AszFQSg9vej14l7LW8/M9JFU0+wv7bIqVZKCgoxHYGDh5SsJOxe38fc3+yuFMwhZAAAAFZTNZoSitDTHj7zQ42xQOnvW7K+oaL6++cHn0iBU1LaStPHjr2pchO4AAABQzuTkGOGmqHCUF5CKez2vjafNEle5sjEJQXCwFBIiBQfb5O+frfDwSgoJsdhfCw4uWRCqVIlT3+A+hCwAAAA3sdmM64BSU42L7FNSCi+npl4+HJ07Z+7XkcffPy8IXRyKil++3GuXjghZrTYlJZ1RjRo15ONDSkL5QMgCAABwks1mjP4UF5IcLV+8np1tVvWGwECpalXnHnkhqKhQVKmSuV8L4KkIWQAAoELJyTHCzpkz0unTxiNv+eJnRyEpNdWc0+t8fAoHoJAQ58PSxaGJa4eAssePGQAAKHdsNmOiBUfh6OJnR9vS0txbq8UiVatmPEJDjUdRy6GhRhiqVq1gOAoM5HoioDwhZAEAAFNduGCEn1OnpORkx8+nThUOTTk57qnPz69gCCouJF0amKpVM0acfHzcUysAz0DIAgAALnPhQsFgVFxoyltOTS37unx9perVpbAw4/niZUfPYWH5QalKFUaRAJQMIQsAABQpM1NKSir4OHlSOnHCokOHqikjw1IgQJX1qXhVqxYORZcLTNWrG9ciEZQAuAshCwCACuTCBSMQOQpOjrZlZBR1JIukKldUS/XqUni4FBGR/3zx8qXbqldn0gYA5QMfVQAAlHM5OUYoOn5c+usv43Hx8sXB6cwZ17+/xVIwMBUXlPKew8IITAC8Fx9vAAB4IJvNuFYpLyhdGpwuXj91ymjvSuHhUo0aUmSk8Zz3yFuPiLDK1zdZTZuGKzzcR76+rn1/ACjPCFkAALiRzWZcu3TsmHT0qPE4dsxxiDp/3nXvGxLiOCw5DlCXH2WyWqWkpFxFRDBzHgBcyuNC1ubNm/Xkk09q586dqlGjhuLi4vTYY485bJuenq4XXnhBixYtUmZmpq6++mpNnz5d1157rZurBgDACEUXh6e8AHXpelaWa96vUiWpVi2pdm3j+dLlvEfNmlLlyq55TwDA5XlUyDpz5oy6d++uuLg4jRgxQps2bVK3bt3UsGFDde7cuVD74cOH68SJE9q+fbuqVaumKVOmqHv37tq/f7+CgoJM+AoAAN4qI0M6dEg6fNh4PnKkcJBKTnbNe4WHFw5LjoJUaCgz5gGAJ/KokLVw4UKFhYVp1KhRkqT27durX79+SkhIcBiysrKyNGHCBEVGRkqSnn32WU2ePFl79uxhNAsA4LQLF4yQlBegHD27YsKIsDCpbl2pTh3jOe9Rp44RnGrXNk7Xq1Tpyt8LAGAejwpZiYmJio2NLbAtNjZW7733nsP2n376aYH1r776SqGhoWrcuLHD9llZWcq66ByNtP/dzMNqtcpqtV5J6UCxrFarbDYb/Qxljr5WmM1mBKSDBy8OThYdPiz749gxyWYr/ZCQv7/NHpzyA5RNtWsXDFKBgc4drzz889HX4C70NbiLK/uYR4Ws9PT0Qqf5BQUFKaPom3TYffXVVxo+fLjefvtthYSEOGwzdepUTZw4sdD2kydPKjs7u3RFA06wWq1KTU2VzWaTD1eIowxV1L529qxFhw752h+HDxd8zsgo/ffC39+m2rVzVbeuVXXq5Kpu3dz/PVtVq1auatWyqnp162Unf8jIKO6eU+VPRe1rcD/6GtwlNTXVZccyNWTFx8crPj7evn7DDTcoNDS0QJuzZ88WGZryTJs2TRMmTNCsWbP06KOPFtlu7Nix9lMRJWMkKzo6WpGRkYXeF3Alq9Uqi8WiyMhIfkGgTHlrXzt/XvrzT+nAAePx558WHThgjE4dOCAlJ5d+FKpmTZvq1ZOioqR69aToaJuio6XoaGO9Zk3973vpIw/7v0lTeWtfg+ehr8FdKrnwXG1Tf1vExcUpLi7Ovj5nzhy9+uqrBdrs2LFDrVq1crh/VlaW+vfvr/Xr12vVqlW68cYbi32/gIAABQQEFNru4+PDDy3KnMVioa/BLcprXztzRtq7V/rjD+N5715p3z4jSB07Vrpj+vlJ9etLV10lxcQYy0aQkj1YBQRcGtCYScJZ5bWvofyhr8EdXNm/POq/5Hr37q3nnntOM2fO1OOPP67Vq1drwYIF+vbbbx22HzRokHbv3q0tW7aoZs2abq4WAFASNptx09y8AHXp4/Tpkh/TYjGCUl6Iuuqq/EdMjHEtFDfJBQC4m0eFrPDwcC1evFgjRozQ6NGjVatWLc2YMUOdOnWSJK1du1bdu3fX7t27lZ2drY8//liVKlVSw4YNCxxn6dKl6tixowlfAQAgLU3as0f67Tfj+eIgVZrT3WvWLByg8kJUvXrMxAcA8DweFbIkY9r2rVu3OnytY8eOBSbBsNls7ioLAHCR3Fxjpr68IJX3vGePdPx4yY5lsRin7zVqVPjRoIHEbQ8BAOWNx4UsAIDnyMgwAtSlYer336WL7ohxWT4+xsiToyB11VVS5cpl9iUAAOB2hCwAgDIzpV9/lXbtknbuzH/+88+SHadGDalpU6lZM+O5aVOpSRMjYHFaHwCgoiBkAUAFkpVljERdHKZ27TJm8XP2DGx/f2ME6uIwlfccFla29QMAUB4QsgDAC9lsxv2jtm2Ttm/PD1R//GFcT+WMkBCpZUupRQupefP8MHXVVcbU6AAAwDF+TQJAOZeVJe3ebQSqX36xaPPm6vr1V4vTM/kFBhpBqmVLqVWr/OeoKGNSCgAAUDKELAAoR5KTjZGpbdvyH7/+KuXk5LWwSHJ88VNAgDEidXGYatnSuF6K+3sCAOA6hCwA8FB//SVt2SJt3iz98osRqA4fdm7fqCib2rSxqE0b6eqrpdhYYzp0TvMDAKDs8esWADxAcrL0889GoNqyxXgcOXL5/Xx9jVP92rQxHq1bW1Wnzkk1bx4pHx/O9QMAwAyELABws4yM/CCVF6r277/8flWrGqNSeYGqTRsjYF18jymrVUpK4kbtAACYiZAFAGXIZpP27pXWr89/JCYaYag4ISFS27bS9ddL111nPK66iokoAAAoDwhZAOBCGRnSpk1GmNqwwXicOlX8PlWqSNdckx+orr9eatyYySgAACivCFkAcAWOHpXWrpXWrJF++unyo1Q+PsbMfjfeKN1wgxGqWrRgQgoAALwJv9YBwEk2m7RvX36oWrPm8tdSVa8u3XSTEapuuklq1844FRAAAHgvQhYAFMFqNW7ymxeo1qyRjh8vun3eKNVNN+U/GjfmOioAACoaQhYA/I/NJv3+u/TDD9KKFdKPP0qnTxfdPiDAOOXvllukjh2NUMUoFQAAIGQBqNCOHTMC1YoVRrg6erTotsHBUvv2RqC65RZjgoqLp08HAACQCFkAKpjUVGn16vxQ9euvRbcNCzPCVN6jTRsmqAAAAJfHnwsAvJrVKv38s7RkibRsmTG9elGz/1WpYoxSde4sdelihCqmUQcAACVFyALgdc6ckb7/3ghWS5dKSUmO2/n4GLP95YWqm24yrrMCAAC4EoQsAOWezWbcn2rJEuPx009Sbq7jts2bG4GqSxfp1lulatXcWysAAPB+hCwA5dK5c8Y1VYsXG8HqyBHH7YKCjEDVo4fUvbsUHe3eOgEAQMVDyAJQbpw+LX37rbRokXF9VWam43ZNmhih6s47jWusOAUQAAC4EyELgEc7dEj66ivpyy+NmwE7Og0wIEC67bb80apGjdxfJwAAQB5CFgCPc/Cg9Nln0qefSlu2OG4TGSndc490993GxBWBgW4tEQAAoEiELAAe4c8/84PV5s2O2zRoIN17r9SrlzEToK+vW0sEAABwCiELgGmOHDFC1aefShs3Om7Tpo3Uu7cRrFq1kiwWd1YIAABQcoQsAG6VmiotXCh99JG0apUx/fql2rSR7rvPeDRu7PYSAQAArgghC0CZy86Wli83gtXXX0vnzxduc/XV+cGqSRP31wgAAOAqhCwAZcJmMyateP996ZNPpOTkwm0aNZIeflh68EGpaVO3lwgAAFAmCFkAXOrUKWn+fGnuXCkxsfDrERFSv37SI49I7dpxjRUAAPA+hCwAVyw3V/rhByNYffWVcXrgxSpXNiaueOQRqWtXyd/flDIBAADcgpAFoNSOHJHmzJESEqTDhwu/ftNN0uDB0v33S1Wrur8+AAAAMxCyAJSIzSatXCm9844xiUVubsHXa9SQBgyQBg2SWrQwp0YAAAAzEbIAOCUlRZo3T5o5U9qzp+BrPj5Sjx7GqFXPnpwOCAAAKjZCFoBi7dghvf22MZnFuXMFX6tdW3rsMelvf5Pq1jWnPgAAAE9DyAJQiM0mLVsmTZ9uTGhxqU6dpOHDjcksGLUCAAAoyMfsAi61efNmtWvXToGBgYqJidHs2bOd2m/ZsmXy8fHRwYMHy7ZAwIudP2/MENiqlXH638UBKzhYevJJaedOadUq46bBBCwAAIDCPGok68yZM+revbvi4uI0YsQIbdq0Sd26dVPDhg3VuXPnIvc7duyYBg0aJJvN5sZqAe9x6pRxrdU770hJSQVfa9hQGjlSevRRKSTElPIAAADKFY8ayVq4cKHCwsI0atQo+fv7q3379urXr58SEhKK3Mdqterhhx/WE0884cZKAe9w6JD01FNSdLQ0YULBgNW+vbRwoTHJxVNPEbAAAACc5VEjWYmJiYqNjS2wLTY2Vu+9916R+0yaNElRUVEaMGCAJkyYUOzxs7KylJWVZV9PS0uTZAQ1q9V6BZUDxbNarbLZbB7Tz/bvl15+2aJ586QLFyz27T4+NvXuLY0aZdMNN+S395Cy4QRP62vwXvQ1uAt9De7iyj7mUSErPT1dQUFBBbYFBQUpIyPDYfvVq1fr448/1pYtW5ScnHzZ40+dOlUTJ04stP3kyZPKzs4uXdGAE6xWq1JTU2Wz2eTjY94A8h9/+Oqtt4L15ZeVlZubH64CA6166KFM/e1v51SvnnHjq0tPG0T54Cl9Dd6PvgZ3oa/BXVJTU112LFNDVnx8vOLj4+3rN9xwg0JDQwu0OXv2rEIcnKd08uRJDRw4UJ9//rlCQkKcClljx47VqFGj7OtpaWmKjo5WZGRkofcFXMlqtcpisSgyMtKUXxA7dkjx8RZ9/rlks+WHq6pVbXrqKenvf5ciIqpIquL22uBaZvc1VBz0NbgLfQ3uUqlSJZcdy9SQFRcXp7i4OPv6nDlz9OqrrxZos2PHDrVq1arQvsuXL1dSUpK6dOkiKX94LzY2VnFxcRozZkyhfQICAhQQEFBou4+PDz+0KHMWi8XtfW3PHmn8eOmzzwpur17dmMxixAiLjP9fsBTeGeWWGX0NFRN9De5CX4M7uLJ/eVRP7d27t5KSkjRz5kxZrVatXLlSCxYs0JAhQwq1feSRR3Tu3DmlpKQoJSVFO3bskGSEMkcBC6hIDh+Whg6VWrYsGLBq1JCmTZMOHjTCFwO4AAAArudRISs8PFyLFy/Wv//9bwUFBWnIkCGaMWOGOnXqJElau3atgoODdejQIXMLBTzUqVPS6NFS48bG/a5yjcurVKOG9Oab0oED0nPPMVMgAABAWfKoiS8kqX379tq6davD1zp27FjkJBgxMTHcJwsVVnq6NH269PrrxnKeqlWl5583rrkKDjavPgAAgIrE40IWAOfl5kr//rdx6t/Jk/nbK1eWnn5aeuEF4/orAAAAuA8hCyinVq82Jq/Yvj1/m5+fcS3W+PFSnTpmVQYAAFCxXdE1WTk5OTpx4oQuXLjgqnoAXMaBA1KfPtJttxUMWPffL/36qzRrFgELAADATCUOWStWrNCwYcNUv359BQQEqE6dOqpcubLq1KmjQYMGafny5WVRJ1DhZWRI48ZJzZtLCxfmb7/2WmntWumTT6RGjcyrDwAAAAanTxdcsWKFXnjhBW3btk1XX321evXqpejoaIWGhio9PV1Hjx7Vxo0bdffddys2NlavvvqqfVZAAKVns0kffWRcX3X8eP72mjWl+Hhp4ECJ24YAAAB4DqdC1vDhw7Vo0SI98cQT+uabb1S7du0i2548eVIJCQl66KGH1Lt3b7399tsuKxaoaP74Q3r8cWnlyvxt/v7SM88Yo1pVq5pXGwAAABxz6v+/q1Wrpt9//13jx48vNmBJUmRkpJ5//nnt2bNHVfkLECiV7GxjlKp164IB6557pN27pVdeIWABAAB4KqdGsqZOnVriA4eEhCg+Pr7E+wEV3fr10mOPSTt35m+rX1+aOVPq0cO8ugAAAOCcUl3JceTIET322GNq1KiRgoKC9Msvv+iFF17Qhx9+6Or6gAojNVV68kmpffv8gOXjI40eLe3aRcACAAAoL0ocsv744w+1adNGP/30k7p3767z58/LZrMpNzdXAwcO1BdffFEWdQJe7euvpRYtjNEqm83Y1rattHmz9NprUlCQufUBAADAeSUOWc8995zatm2r7du364033pDtf38Rvvbaaxo8eLCmTZvm8iIBb5WWJg0ZYlxrdeyYsS0wUJo+XdqwwZieHQAAAOWL01O451m1apU+/vhj+fr6Kjc3t8Br/fr10yeffOKy4gBvtnatNGCAdPBg/rYePYzRrPr1TSsLAAAAV6hU12SdO3fO4fa0tDT5+vpeUUGAt8vKMu55deut+QErJERKSJC+/ZaABQAAUN6VOGR16NBBkyZN0qlTp+zbLBaLrFarZs6cqY4dO7q0QMCbJCZK7dpJ06blX3vVsaO0fbtxU2GLxdTyAAAA4AIlPl3wlVdeUYcOHdSkSRN169ZNFotFr732mnbt2qX9+/dr3bp1ZVEnUK5ZrdK//hWoqVMtys42tvn7S1OmGLMHMgAMAADgPUo8ktWqVSv9/PPP6tmzp9asWSNfX199//33atq0qTZs2KDY2NiyqBMot06ckP7v/yyaOLGqsrONoapWrYyZA59/noAFAADgbUo8kiVJDRs21Lx581xdC+B1Vq2SHnpI+usvI1xZLDaNHm3R5MlS5comFwcAAIAyUaqJL3Jzc/Wf//xHQ4cO1Z133qm9e/fqo48+0q+//urq+oByKTdXmjRJ6tJF+usvY1uNGrn6/nubXn2VgAUAAODNShyy0tPT1bFjRw0ePFibNm3SsmXLlJaWps8//1w33nijtm3bVgZlAuVHcrJ0553ShAnGtViS1KWLTStWJOu228ytDQAAAGWvxCFr3LhxSk5O1p49e7R161b7zYg/+eQTtWnTRuPHj3d5kUB58csv0nXXScuXG+s+PtJLL0lLl9oUEWE1tzgAAAC4RYlD1meffaYJEyaofv36slw033RAQIBGjx6t9evXu7RAoLyYN0+6+eb8e19FRkorVkhxcUbYAgAAQMVQ4j/9UlNTVb16dYevBQQEKDMz84qLAsqTnBzpmWekRx+Vzp83tt1wg7R1q9Spk6mlAQAAwASlmsJ9zpw5Dl/76quv1Lp16ysuCigvUlOlnj2lN9/M3zZsmPTjj1JUlGllAQAAwEQlnsI9Li5Offr0UceOHfXwww/LYrHoxx9/1Ny5czV79mx99tlnZVEn4HH++EO6+27pt9+MdT8/6Z13pMceM7cuAAAAmKvEI1m9evXSxx9/rMOHD2v48OGy2WwaPXq0vvzyS82dO1f33ntvWdQJeJQ1a4xTAvMCVni49MMPBCwAAACUYiRrz549uv/++3X//ffrjz/+0MmTJxUaGqrmzZsXmAgD8FYLFhjXX2VnG+stWkjffCM1aGBuXQAAAPAMJR7J6tKliz744ANJUuPGjXXzzTerRYsWBCx4PZtNmjZNevDB/IDVrZu0fj0BCwAAAPlKHLIyMzOLnF0Q8Fa5udJTT0kvvJC/behQYwSralXz6gIAAIDnKfHpgtOnT9eoUaN0+vRptW3bVlUd/IVZr149lxQHeIKsLKl/f+niOV2mTDHuf8UALgAAAC5V4pA1ZMgQ5ebmatCgQUWeIpibm3vFhQGeICND6t1b+v57Y93PT3rvPSN0AQAAAI6UOGTNmTOH669QIZw+Ld15p7Rhg7FepYr0xRdS9+7m1gUAAADPVuKQdfvtt6t27dry9/cv9FpmZqa2b9/uksIAM504IXXpIu3caayHhkrffiu1b29qWQAAACgHSjzxxVVXXaVt27Y5fG3z5s3q3LnzldYEmOr4calTp/yAVbOm9OOPBCwAAAA4x6mRrNGjR+vMmTOSJJvNpkmTJikyMrJAG5vNpq1btyo0NNTlRQLucuSIdPvt0h9/GOv16kkrVkiNGplbFwAAAMoPp0JW8+bN9dJLL9nXf/75ZwUEBBRo4+Pjo9DQUL355psuLRBwlz//NALW/v3GekyMtGqV8QwAAAA4y6nTBYcOHaoDBw7owIEDqlu3rpYuXWpfz3vs27dPP//8s+67774rKmjz5s1q166dAgMDFRMTo9mzZxfbfv78+WratKmCgoLUsmVLffnll1f0/qiYjhyRbrstP2A1bGicIkjAAgAAQEmV+JqsmjVr6sCBA2VRi86cOaPu3burX79+Sk1N1fz58zVq1CitWLHCYfvvvvtOjz/+uN544w2lp6dr0qRJuv/++3X48OEyqQ/e6a+/pM6dpbxu3bixEbC43RsAAABKo8Qh69dff1VQUFBZ1KKFCxcqLCxMo0aNkr+/v9q3b69+/fopISHBYfu33npLTzzxhHr06CEfHx/16dNHGzZs4LowOO3UKemOO6TffzfWGzaUVq+W6tY1tSwAAACUYyWewn3w4MF65ZVX1KRJE9WvX9+lxSQmJio2NrbAttjYWL333nsO22/atEk33XSTbr/9dm3fvl2NGjXSq6++qpCQEIfts7KylJWVZV9PS0uTJFmtVlmtVhd9FSgvUlKkbt0s2rnTuO9bvXo2ff+9TbVqSa7uDlarVTabjX6GMkdfg7vQ1+Au9DW4iyv7WIlD1m+//aZ169apQYMGCgsLU9WqVQu8brFYtG/fvlIVk56eXmiULCgoSBkZGQ7bnz59WjNnztTChQt1zTXXKCEhQT169NDOnTsV4+BimqlTp2rixImFtp88eVLZ2dmlqhnl07lzUr9+1bV1ayVJUs2auVqw4LSqVMlVUpLr389qtSo1NVU2m00+PiUeQAacRl+Du9DX4C70NbhLamqqy45V4pAVFRWlBx980CVvHh8fr/j4ePv6DTfcUOhUv7NnzxY5MlW5cmUNHjxYN9xwgyRp2LBheuutt7R48WI9+eSThdqPHTtWo0aNsq+npaUpOjpakZGRnGJYgeTkSEOHWrR5szGCFRlp04oVFjVvHl5m72m1WmWxWBQZGckvCJQp+hrchb4Gd6GvwV0qVarksmOVOGQVdX1UacTFxSkuLs6+PmfOHL366qsF2uzYsUOtWrVyuH/Tpk117ty5AttycnKK/AYFBAQUmnpeMqaf54e2YrDZpCeekBYvNtZDQqRlyyxq2dJS5u9tsVjoa3AL+hrchb4Gd6GvwR1c2b9KfaTTp0/r8OHDOnTokA4dOqSDBw9q165deuedd0pdTO/evZWUlKSZM2fKarVq5cqVWrBggYYMGeKw/WOPPaZ///vfWrNmjXJycvTOO+/oxIkT6tmzZ6lrgHf7f/9PyrvEr1IladEi6dprTS0JAAAAXqbEI1nbtm1Tnz59dPDgwSLbODpVzxnh4eFavHixRowYodGjR6tWrVqaMWOGOnXqJElau3atunfvrt27d6tevXoaNmyYfH199fjjj+vo0aNq3ry5li5dqtq1a5fq/eHd3nlHyjs71WKRPvzQuPkwAAAA4EoWm81mK8kOd9xxh3bt2qXnnntOS5YskZ+fnzp37qxvv/1Wu3fv1k8//aRGjRqVVb0ulZaWpmrVqunMmTNck+XlliyR7rorf9bAGTOkp55y3/tbrVYlJSWpRo0anOqAMkVfg7vQ1+Au9DW4S0pKisLCwpSamlpocr+SKnFP/fnnn/Xqq6/qmWee0YMPPqhz587p2Wef1erVq9WuXTv95z//uaKCAFfbsUN64IH8gDVmjHsDFgAAACqWEoesrKws+/ToTZs21bZt2+yv/e1vf9MHH3zgqtqAK/bXX1LPnlLeXQD69pVeesncmgAAAODdShyyoqOjtXfvXklGyEpPT9f+/fslGfe0On78uGsrBErp3Dnp7rulw4eN9euvlz74QOJMAwAAAJSlEv+5+cADD2js2LH64osvFBERoVatWmnixInatWuXpk+fXm6ux4J3s9mkIUOkzZuN9Xr1pK+/lgIDza0LAAAA3q/EswuOGzdO+/fv15w5c9SnTx+99NJLuv/++/XRRx/J19dXCxYsKIs6gRKZPl3K64rBwdI330i1aplbEwAAACqGEoesSpUq6cMPP1ROTo4k6a677tKvv/6qrVu3KjY2lpEsmO6HH6Tnn89f//BDKTbWvHoAAABQsZQ4ZNl39MvfNSYmxj4ZBmCmgwelfv3yZxIcP17q1cvMigAAAFDROBWyBg8e7PQBLRaL5s6dW+qCgNI6d066914pOdlY79FD+sc/TC0JAAAAFZBTIev9998vtM1iscjRfYwJWTDLiBFS3h0FGjWS5s9nJkEAAAC4n1N/glqt1gKP7Oxs2Ww2bdmypdBrubm5ZV0zUMhHH0nvvWcsBwVJixZJoaFmVgQAAICKqlT/z2+xWFxdB1Bqv/0mPf54/vqsWVLLlubVAwAAgIqNk6lQrmVmSvffL509a6wPGiT1729uTQAAAKjYCFko10aOlBITjeUWLaQZM0wtBwAAACBkofz6/HNp9mxjuUoV6dNPjeuxAAAAADNdUcji2iyY5dgxadiw/PW33+Y6LAAAAHgGp6Zwb9CggcPtd911lypVqlRgm8Vi0b59+668MqAINps0eLB0+rSxft99xrVYAAAAgCdwKmTVq1ev0KhV/fr1y6Qg4HJmzpSWLzeWa9c2ZhNkUBUAAACewqmQtXr16jIuA3DOb79Jzz2Xv56QIIWHm1cPAAAAcCmnrslKTk4u1cFLux/gyIULxvTsmZnG+lNPSd26mVsTAAAAcCmnQlabNm00ffp0XbhwwamDZmZm6vXXX9e11157RcUBF3vtNWnLFmO5aVPplVfMrQcAAABwxKmQtWbNGn399deqW7eunnvuOa1Zs0Zn8+7++j+pqalasmSJnnrqKdWpU0dfffUVpxnCZX77TZo40Vj28ZE+/FAKDDS3JgAAAMARp67Juuqqq7R69WotWrRIL730kl5//XVZLBZVrVpVISEhSklJ0dmzZ2Wz2XT99dcrISFBvXr1KuPSUVFYrdLQoVJWlrE+erR0/fXm1gQAAAAUxamQladXr17q1auX9u/fr++++06HDh1ScnKywsPD1aBBA3Xt2lX16tUrq1pRQc2aJf33v8Zyo0bSP/5hajkAAABAsUoUsvI0aNBAjz/+uKtrAQr5809pzJj89TlzOE0QAAAAns2pa7IAM9hs0uOPSxkZxvpjj0mdOplaEgAAAHBZhCx4rM8/l5YtM5br1JGmTTO3HgAAAMAZhCx4pIwM6Zln8tffeUeqVs28egAAAABnEbLgkSZNko4eNZZ79JDuucfcegAAAABnEbLgcXbvlt54w1gOCJDeekuyWMytCQAAAHBWqWYXXL9+vZYtW6Z9+/bZp3CvV6+e/u///k8dO3aUhb+IUUo2m/TUU1JOjrH+wgtSw4bm1gQAAACUhNMjWVlZWXrnnXcUExOj9u3b66233tK2bduUnp6uxMREzZkzR506dVJ0dLTeeecdXbhwoSzrhpf65BNp1SpjOSam4PTtAAAAQHng1EjWhg0bNGDAANlsNg0fPlzdu3dX69atC7Xbt2+fvv76a82aNUszZszQvHnz1K5dO5cXDe909qw0enT++ltvSVWqmFcPAAAAUBpOhaz+/ftr6tSp6tu3b7HtGjZsqGeeeUbPPPOMPv30Uz3yyCP6/fffXVIovN9rr0nHjhnLPXtKd91lbj0AAABAaTh1uuDOnTvtAWv16tVKT0+/7D7333+/du7ceWXVocI4diz/Plh+ftLrr5tbDwAAAFBaToWsgIAA+/L999+vb775xqmDV6pUqXRVocJ58UXp3Dlj+fHHpSZNzK0HAAAAKK0ST+Hu7+8vH5+ym/l98+bNateunQIDAxUTE6PZs2cX2TYzM1PDhw9XrVq1FBYWpttvv12JiYllVhvKxo4d0nvvGctVq0oTJphbDwAAAHAlSjyF++TJkzVy5Ejt2bNHbdu2VdWqVQu1ueWWW0pVzJkzZ9S9e3fFxcVpxIgR2rRpk7p166aGDRuqc+fOhdq/8sor+vHHH7V161bVrFlTb775pnr06KFDhw4xjXw58txzxtTtkjRunBQRYW49AAAAwJUoccgaOnSoJGnixImSVCDM2Gw2WSwW5ebmlqqYhQsXKiwsTKNGjZIktW/fXv369VNCQoLDkBUUFCSbzSar1SrJGGU7cuSITp8+rfDw8FLVAPdatkz67jtjuX596emnza0HAAAAuFIlDlmr8m5iVAYSExMVGxtbYFtsbKzeyzuX7BKjRo3S2rVrFR0dLV9fX9lsNv39738vMmBlZWUpKyvLvp6WliZJslqt9qAG97Fapeeft0gygnp8vFWVKhnbvY3Vai3wHwJAWaGvwV3oa3AX+hrcxZV9rMQh69Zbb3XZm18qPT1dQUFBBbYFBQUpIyPDYfsxY8Zo7969+u2331S/fn3961//Umpqqn1E7VJTp061j8Bd7OTJk8rOznbNFwGnLVpUWYmJoZKkNm2yddttp5WUZG5NZcVqtdr7Zlle0wjQ1+Au9DW4C30N7pKamuqyYzkVsjp06KA333xT1113ndMH/vnnnzVy5EitXbu2yDbx8fGKj4+3r99www0KDQ0t0Obs2bMKCQlxuP/cuXP1zjvvqGnTppKkkSNHqkmTJoqNjdW9995bqP3YsWPtpyJKxkhWdHS0IiMjC70vylZOjvTGG/lB+JVX/FSzZg0TKypbVqtVFotFkZGR/IJAmaKvwV3oa3AX+hrcxZUzozsVskaOHKk777xTN9xwg4YNG6auXbvK39+/ULv09HQtX75c7777rrZv366ZM2cWe9y4uDjFxcXZ1+fMmaNXX321QJsdO3aoVatWDvcPCAgoNGLl6+urgwcPFtn+4uno8/j4+PBD62b/+Y+Ud5/qW2+V7rjDR94+V4nFYqGvwS3oa3AX+hrchb4Gd3Bl/3LqSH379tWuXbvUoEED3XfffapataratWune++9VwMGDNDdd9+ta665RtWrV9fAgQPVsmVLJSYm2m9g7KzevXsrKSlJM2fOlNVq1cqVK7VgwQINGTLEYfsBAwZo0qRJ+uOPP5STk6N//vOfOnDggLp161ai94V7ZWdLF5+1OXmyvD5gAQAAoOJwOq5FRETozTff1OHDh/X222+rQYMGOnHihDZu3KhTp06pZcuWmjt3rg4dOqQ333xTNWvWLHEx4eHhWrx4sf79738rKChIQ4YM0YwZM9SpUydJ0tq1axUcHKxDhw5JkqZMmaK+ffuqS5cuCg8P14IFC7RkyRK1aNGixO8N90lIkPIGG7t2lTp2NLUcAAAAwKUsNlveHYoqnrS0NFWrVk1nzpzhmiw3OX9eatRIOnrUWN+4UWrXztya3MFqtSopKUk1atTgVAeUKfoa3IW+Bnehr8FdUlJSFBYWptTUVIf3Ai4Jp3rq9ddfr3fffVfp6elX9GbAu+/mB6y7764YAQsAAAAVi1Mhy9fXV0888YRq166tQYMGad26dWVdF7xQVpb0yiv565MmmVcLAAAAUFacClkbNmzQnj179Pe//10rV67UrbfeqmbNmum1115Tkrfe2Agu98EH0vHjxvK990pXX21uPQAAAEBZcPrE1saNG+ull17SwYMH9d1336ldu3aaOHGioqOj1bt3by1dulQV+PIuXEZOjjRtWv762LHm1QIAAACUpRJfPWixWNS5c2fNmzdPf/31l959912lpqbqrrvuUr169fTiiy+WRZ0o5z7/XNq3z1ju0kW6/npz6wEAAADKyhVN0RIUFKSBAwdqxYoVWr58uYKDg/XSSy+5qjZ4CZtNmjo1f51RLAAAAHizKwpZR44c0bRp03T11Vera9euys3NJWShkCVLpB07jOV27aTbbjO3HgAAAKAs+ZV0h9TUVH322WeaP3++1q5dq8qVK6tPnz6aMWOGbrnllrKoEeXcpaNYFot5tQAAAABlzamQlZ2drW+//Vbz58/XkiVLlJWVpeuvv14zZ87Ugw8+qJCQkLKuE+XU2rXSf/9rLLdoYdwbCwAAAPBmToWsmjVrKi0tTeHh4XriiSc0ZMgQtWzZsqxrgxe4eEbBMWMkbtQOAAAAb+dUyLrppps0ZMgQ3X333fL39y/rmuAl9u6VFi82lqOjpX79zK0HAAAAcAenQtaSJUvKug54oRkzjJkFJenJJyXyOQAAACoCTt5CmUhLkxISjOUqVaS//c3cegAAAAB3IWShTCQkSOnpxnL//lL16ubWAwAAALgLIQsul5trnCqY5+mnzasFAAAAcDdCFlxuyRJp3z5juUsXiYkoAQAAUJEQsuBy//xn/vLf/25eHQAAAIAZCFlwqZ07pRUrjOVGjaQePcytBwAAAHA3QhZcaubM/OURI7j5MAAAACoe/gSGy5w9K330kbEcGCgNHGhqOQAAAIApCFlwmU8/zZ+2/cEHpapVza0HAAAAMAMhCy4zZ07+MjcfBgAAQEVFyIJL7NwprV9vLMfGSu3amVsPAAAAYBZCFlzi0lEsi8W8WgAAAAAzEbJwxTIzpXnzjOXKlaWHHza3HgAAAMBMhCxcsS++kFJSjOX775fCwkwtBwAAADAVIQtXjAkvAAAAgHyELFyR336T1qwxlps3l9q3N7ceAAAAwGyELFyRDz7IXx46lAkvAAAAAEIWSs1qlebPN5Z9faX+/c2tBwAAAPAEhCyU2po10uHDxvL//Z8UGWluPQAAAIAnIGSh1D76KH/5kUfMqwMAAADwJIQslMr589JnnxnLwcHS3XebWw8AAADgKQhZKJVvv5XS0ozlPn2kwEBz6wEAAAA8BSELpcKpggAAAIBjhCyUWHKytGSJsVynjnTbbebWAwAAAHgSjw1ZGzZsUEBAwGXbTZs2TXXr1lVQUJBuvfVW/frrr26ormL79FPpwgVj+aGHjOnbAQAAABg8LmRZrVYlJCSoa9euys7OLrbtvHnzNH36dC1ZskQpKSm64YYb1LNnT13ISwAoE5wqCAAAABTNz+wCLjVkyBD99ttvmjJliv7+978X23bOnDkaMWKErr76aknSpEmTNHPmTP3444/q0qVLofZZWVnKysqyr6f9b+YGq9Uqq9Xqwq/Ce+3fL/30k5HNW7WyqVUrm/jWXZ7VapXNZqOfoczR1+Au9DW4C30N7uLKPuZxIWvy5MmKiorS6tWrL9s2MTFRzz//vH29cuXKatKkiXbu3OkwZE2dOlUTJ04stP3kyZOXHTWD4f33gySFSJLuvjtDJ0+eNbegcsJqtSo1NVU2m00+Ph43gAwvQl+Du9DX4C70NbhLamqqy47lcSErKirK6bbp6ekKCgoqsC0oKEgZGRkO248dO1ajRo2yr6elpSk6OlqRkZEKDQ0tVb0VzfLlFvvyoEFBqlEjqJjWyGO1WmWxWBQZGckvCJQp+hrchb4Gd6GvwV0qVarksmOZGrLi4+MVHx9vX1+6dKk6duzo9P4hISE6e7bgSMrZs2cVEhLisH1AQIDDyTR8fHz4oXXCn39KW7YYy9dcIzVqxPesJCwWC30NbkFfg7vQ1+Au9DW4gyv7l6k9NS4uThkZGfZHSQKWJLVs2VKJiYn29aysLP3+++9q1aqVq0uFpC++yF/u08e8OgAAAABPVq7/O2Dw4MF6++239fvvvyszM1MvvPCCateurVtvvdXs0rzSxSGrb1/z6gAAAAA8WbkKWWvXrlVwcLAOHTokyZiJ8IknntCtt96qiIgIbd++XYsXL5afn8ddalbuHT0q/fSTsdyypdS0qbn1AAAAAJ7KY9NIp06dZLPZCmzr2LFjoUktxo8fr/Hjx7uztArpyy/zlzlVEAAAAChauRrJgnk+/zx/mVMFAQAAgKIRsnBZJ05Ia9cay40bS8wrAgAAABSNkIXLWrRIyrsBdt++ksVSbHMAAACgQiNk4bKYuh0AAABwHiELxTp9Wlq50liOiZGuvdbUcgAAAACPR8hCsZYulXJzjeXevTlVEAAAALgcQhaKtXhx/nLPnubVAQAAAJQXhCwUKSdHWrbMWK5aVerQwdx6AAAAgPKAkIUibdggnTljLHfrJvn7m1sPAAAAUB4QslCki08VvPNO8+oAAAAAyhNCFoqUF7IsFql7d3NrAQAAAMoLQhYcOnRISkw0lq+/XqpRw9x6AAAAgPKCkAWHlizJX+ZUQQAAAMB5hCw4xPVYAAAAQOkQslBIZqa0YoWxXKuWdM015tYDAAAAlCeELBSyerURtCSpRw/Jh14CAAAAOI0/n1EIpwoCAAAApUfIQgE2W37I8veX7rjD3HoAAACA8oaQhQL++EM6eNBY7thRCgkxtRwAAACg3CFkoYC8CS8kqWtX8+oAAAAAyitCFgq4OGR17mxeHQAAAEB5RciCXW6utGqVsRwWxtTtAAAAQGkQsmC3bZt0+rSxfNttkq+vqeUAAAAA5RIhC3acKggAAABcOUIW7AhZAAAAwJUjZEGSlJUlrV1rLNetKzVpYm49AAAAQHlFyIIkacMGKTPTWO7SRbJYzK0HAAAAKK8IWZAk/fBD/jKnCgIAAAClR8iCJK7HAgAAAFyFkAWlpUmbNhnLzZpJdeqYWw8AAABQnhGyoDVrjBsRS4xiAQAAAFeKkIUCpwp26WJeHQAAAIA3IGTBPumFj4/UqZOppQAAAADlHiGrgjt9Wtq501i+9lopNNTUcgAAAIByj5BVwf30U/5yx47m1QEAAAB4C48NWRs2bFBAQECxbdLT0zV8+HDVqVNHYWFh6tSpk7Zu3eqmCr3DunX5yx06mFcHAAAA4C08LmRZrVYlJCSoa9euys7OLrbt8OHDtXfvXm3fvl0nTpzQLbfcou7du+vs2bNuqrb8uzhktW9vXh0AAACAt/C4kDVkyBDNnj1bU6ZMuWzbrKwsTZgwQZGRkapUqZKeffZZJSUlac+ePW6otPw7f17avNlYbtRIqlnT3HoAAAAAb+BndgGXmjx5sqKiorR69erLtv30008LrH/11VcKDQ1V48aNHbbPyspSVlaWfT0tLU2SMXpmtVpLX3Q5tXmzlJ1t5Oz27W2yWm0mV+S9rFarbDZbhexncC/6GtyFvgZ3oa/BXVzZxzwuZEVFRZVqv6+++krDhw/X22+/rZCQEIdtpk6dqokTJxbafvLkycuemuiNli8PkmR8r1q3TlNSUqa5BXkxq9Wq1NRU2Ww2+fh43AAyvAh9De5CX4O70NfgLqmpqS47lqkhKz4+XvHx8fb1pUuXqmMppribNm2aJkyYoFmzZunRRx8tst3YsWM1atQo+3paWpqio6MVGRmp0Ao4d/n27Rb7cvfuIapRw3E4xZWzWq2yWCyKjIzkFwTKFH0N7kJfg7vQ1+AulSpVctmxTA1ZcXFxiouLK/X+WVlZ6t+/v9avX69Vq1bpxhtvLLZ9QECAwxkLfXx8KtwPrdWaP317eLjUvLmPLJbi98GVsVgsFbKvwf3oa3AX+hrchb4Gd3Bl//K40wVLYtCgQdq9e7e2bNmimszaUCK//WbciFgyZhUkYAEAAACuUa7+O2Dt2rUKDg7WoUOHtHfvXn388cf6448/1LBhQwUHB9sfa9euNbtUj/ff/+Yvc38sAAAAwHU8diSrU6dOstkKznbXsWNHZWRk2NcvfR3O4/5YAAAAQNkoVyNZcJ28kBUQILVta24tAAAAgDchZFVAx49L+/cby+3aGUELAAAAgGsQsiqgi6/H4lRBAAAAwLUIWRXQxddjMekFAAAA4FqErAro4pGsm282rw4AAADAGxGyKpisLGn7dmO5WTMpLMzcegAAAABvQ8iqYHbskC5cMJavv97cWgAAAABvRMiqYDZvzl8mZAEAAACuR8iqYC4OWdddZ14dAAAAgLciZFUwW7YYz35+Ups2ppYCAAAAeCVCVgVy9qy0e7ex3KqVVKWKufUAAAAA3oiQVYFs3SpZrcYy12MBAAAAZYOQVYHknSoocT0WAAAAUFYIWRUIMwsCAAAAZY+QVYHkhazKlY1rsgAAAAC4HiGrgjhzRtq711hu00by9ze1HAAAAMBrEbIqiJ9/zl/meiwAAACg7BCyKgiuxwIAAADcg5BVQVw8syAhCwAAACg7hKwKIm8kKzhYatLE3FoAAAAAb0bIqgBOnJAOHzaW27aVfH3NrQcAAADwZoSsCoBTBQEAAAD3IWRVAEx6AQAAALgPIasCuHgki+nbAQAAgLJFyKoAduwwnqtVk666ytxaAAAAAG9HyPJyZ87kT3oRGytZLObWAwAAAHg7QpaXS0zMX46NNa8OAAAAoKIgZHm5vFMFJUIWAAAA4A6ELC9HyAIAAADci5Dl5S4OWa1amVcHAAAAUFEQsryY1Zp/TVbDhlJwsLn1AAAAABUBIcuL7d8vnTtnLHOqIAAAAOAehCwvxvVYAAAAgPsRsrwYIQsAAABwP0KWFyNkAQAAAO7nsSFrw4YNCggIcLr9smXL5OPjo4MHD5ZdUeXM9u3Gc2Cg1KCBubUAAAAAFYXHhSyr1aqEhAR17dpV2dnZTu1z7NgxDRo0SDabrYyrKz/S042JLySpdWvJx+P+pQEAAADv5HF/eg8ZMkSzZ8/WlClTnGpvtVr18MMP64knnijjysqXnTvzlzlVEAAAAHAfP7MLuNTkyZMVFRWl1atXO9V+0qRJioqK0oABAzRhwoRi22ZlZSkrK8u+npaWJskIalartdQ1e6Jt26S8DN26tVVe9uWVO1arVTabzev6GTwPfQ3uQl+Du9DX4C6u7GMeF7KioqKcbrt69Wp9/PHH2rJli5KTky/bfurUqZo4cWKh7SdPnnT61MTyYtOmEElBkqSoqDNKSrpgbkEVnNVqVWpqqmw2m3w4dxNliL4Gd6GvwV3oa3CX1NRUlx3L1JAVHx+v+Ph4+/rSpUvVsWNHp/Y9efKkBg4cqM8//1whISFOhayxY8dq1KhR9vW0tDRFR0crMjJSoaGhJa7fk+3da7Ev33prmLzsyyt3rFarLBaLIiMj+QWBMkVfg7vQ1+Au9DW4S6VKlVx2LFNDVlxcnOLi4kq17/Lly5WUlKQuXbpIyh/ei42NVVxcnMaMGVNon4CAAIczFvr4+HjVD63Nlj99e716UvXq3vO1lWcWi8Xr+ho8E30N7kJfg7vQ1+AOruxfHne6oLMeeeQRPfLII/b1gwcP6qqrrtKOHTsUExNjXmEe4NAh6X+XmzHpBQAAAOBm5eq/A9auXavg4GAdOnTI7FI8GjchBgAAAMzjsSNZnTp1KnTfq44dOyojI8Nh+5iYGO6T9T+ELAAAAMA85WokC87ZtSt/uVUr8+oAAAAAKiJClhf67Tfj2ddXatTI3FoAAACAioaQ5WWsVmnPHmO5QQPJwWSKAAAAAMoQIcvLHDkinTtnLDdrZm4tAAAAQEVEyPIyeacKSoQsAAAAwAyELC9DyAIAAADMRcjyMoQsAAAAwFyELC9zcchq2tS8OgAAAICKipDlZfJCVmSkFB5ubi0AAABARUTI8iKpqdLx48YypwoCAAAA5iBkeZG8+2NJhCwAAADALIQsL8KkFwAAAID5CFlehJAFAAAAmI+Q5UUIWQAAAID5CFleJC9kBQRI9eubWwsAAABQURGyvMSFC9LevcZykyaSr6+59QAAAAAVlZ/ZBZjJZrNJktLS0uTjU77z5t69RtCSpAYNpLQ0c+tBQVarVenp6apcuXK572vwbPQ1uAt9De5CX4O7pP3vD+i8jHAlLDZXHKWc2r9/vxo2bGh2GQAAAAA8xL59+9SgQYMrOkaFHsmqXr26JOnQoUOqVq2aydXAm6WlpSk6OlqHDx9W1apVzS4HXoy+Bnehr8Fd6Gtwl9TUVNWrV8+eEa5EhQ5ZeUPO1apV44cWblG1alX6GtyCvgZ3oa/BXehrcBdXnJbKia0AAAAA4EKELAAAAABwoQodsgICAjRhwgQFBASYXQq8HH0N7kJfg7vQ1+Au9DW4iyv7WoWeXRAAAAAAXK1Cj2QBAAAAgKsRsgAAAADAhQhZAAAAAOBCFTZkJSUlqXfv3goJCVFERISefvppXbhwweyy4IU2b96sTp06KSwsTHXq1NGTTz6ps2fPml0WvNyDDz6oTp06mV0GvNS5c+c0bNgwRUREKCwsTHfddZeOHj1qdlnwQlu3blWnTp0UGhqq2rVra8SIEcrKyjK7LHiRU6dOqUGDBlq9erV92+bNm9WuXTsFBgYqJiZGs2fPLvFxK2zI6tevn/z8/HTs2DFt375dK1eu1KRJk8wuC17m1KlT6tatm/r27auTJ09q06ZN2rRpk1544QWzS4MXmzNnjj777DOzy4AX+9vf/qZdu3Zp27ZtOnr0qKpUqaLBgwebXRa8UO/evdWuXTudPHlSiYmJ2r59uyZPnmx2WfAS//3vf3XzzTfrwIED9m1nzpxR9+7d1a9fP6Wmpmr+/PkaNWqUVqxYUaJjV8iQtW/fPq1atUrTp09XSEiI6tatqzFjxighIcHs0uBlDhw4oFtvvVVPPfWU/Pz8FBUVpf79+2vNmjVmlwYvtXPnTk2dOlWPPfaY2aXAS504cUILFizQ7NmzFRUVpcDAQP3rX//Sq6++anZp8EJBQUGy2WyyWq2yWCzy8/PTjh07zC4LXuD999/XQw89pKlTpxbYvnDhQoWFhWnUqFHy9/dX+/bt1a9fvxLnhAoZshITE1W9enVFRUXZt8XGxuro0aNKSUkxrzB4neuvv15ffvmlfd1ms+mbb77R9ddfb2JV8Fbnzp3Tgw8+qHfffVc1atQwuxx4qZ9//lmBgYHasGGDmjRpolq1amnkyJEFfqcCrvKf//xH8+fPV1BQkCIiIrR9+3Y988wzZpcFL/B///d/2rdvn/r06VNge2JiomJjYwtsi42N1c6dO0t0/AoZstLT0xUUFFRgW956RkaGGSWhArhw4YKGDh2qX3/9VVOmTDG7HHihp556Sj169NAdd9xhdinwYqdPn9b58+e1ePFirV+/Xrt27VJSUpL69+9vdmnwMufOndPdd9+t++67T6mpqfrzzz917733ysenQv75CherVauW/Pz8Cm0vKieUNCMUPnIFEBISUmjigbz1kJAQM0qClzt58qTuv/9+/fXXX1qzZo1q165tdknwMvPnz9euXbu0bt06s0uBl6tcubJycnI0bdo0hYeHS5ImT56sG264Qenp6fwehcv88MMPSk5O1uuvvy4/Pz8FBQVp8ODBuvvuu/XXX385/AMZuFIhISE6fPhwgW1nz54t8WdbhfyvgJYtW+r06dMFZkLasWOHoqKiVK1aNRMrgzfasWOHrr32WoWFhWnjxo1q0KCB2SXBC82bN0+7d+9WZGSkQkND9fLLL2vdunUKDQ3VoUOHzC4PXqRp06aSjFGGPDk5OfLx8ZG/v79ZZcELBQQEFNrm6+ur5ORkpaenm1ARKoKWLVsqMTGxwLYdO3aoVatWJTpOhQxZjRs3VocOHTRmzBhlZmbqwIEDmjJlioYOHWp2afAyx44dU+fOndWvXz998cUXqlq1qtklwUstX75c6enpSklJUUpKisaMGaMOHTooJSVF9erVM7s8eJHWrVvrxhtv1DPPPKNTp07pzJkzGj9+vPr06aPKlSubXR68SIcOHVSjRg2NHj1a586dU1JSkuLi4tSxY0eFhYWZXR68VO/evZWUlKSZM2fKarVq5cqVWrBggYYMGVKi41TIkCVJn3zyiVJSUlSjRg1dd9116tGjh8aNG2d2WfAyM2fO1KlTpzRr1iyFhIQoODhYwcHBatmypdmlAUCpffvtt4qJiVFsbKyaNWumevXqleo+MkBxgoKC9N1332n//v2Kjo5WbGysoqOj9fnnn5tdGrxYeHi4Fi9erH//+98KCgrSkCFDNGPGjBLfe9Jis9lsZVMiAAAAAFQ8FXYkCwAAAADKAiELAAAAAFyIkAUAAAAALkTIAgAAAAAXImQBAAAAgAsRsgAAAADAhQhZAAAAAOBChCwAAAAAcCFCFgDAa2zcuFGNGzdWVlaWJMlisRR4+Pr6qmbNmurXr58OHz5c4uMPHDhQMTExJd7v/PnzatSokX766acS7wsAKH8IWQAAr5CVlaX+/fsrPj5eAQEB9u09evTQ+vXrtX79ev3444/65z//qcTERN15553Kzs52S22VK1fW1KlT9eijjyozM9Mt7wkAMA8hCwDgFWbNmqVKlSrpvvvuK7A9MjJSN954o2688UZ16NBB/fr106xZs5SYmKh169a5rb6+ffvKZrPp3//+t9veEwBgDkIWAMBjxcTEaPTo0br99tsVGBio4cOHO2yXk5Ojl19+WY899phTxw0NDZUkZWRk2LdZrVZNmzZNjRs3VqVKlVS/fn2NGTNG58+fL7T/hx9+qGbNmikgIEDNmjXTBx98YH9t9erVslgsmjt3rurUqaOIiAitXLlSFotFf/vb3/Tqq6/KarWW4LsAAChvCFkAAI/29ttvq2XLllq0aJEefPBBh21+/PFHnThxQnfffXeh12w2m3JycpSTk6Ps7GwdOnRI//jHP1S/fn3dcccd9nZDhgzRuHHj9MADD2jx4sV68sknNWPGDPXs2VM2m83e7vDhwxo/frzGjh2rr7/+WrVq1dKgQYOUmJhY4H3Hjh2r1157TW+++abatm0rSerevbsOHz6s9evXu+JbAwDwUH5mFwAAQHFq1aqlt956SxaLpcg23333ncLDwx1OSjFv3jzNmzevwLagoCCtWbNGVapUkSTt3LlT77//vl566SXFxcVJku644w7Vrl1bAwYM0Lfffqu77rpLkjHi9c0336h169aSpAYNGqhJkyZavXq1fZskPf7443rooYcKvG/r1q1VrVo1LVu2TO3bty/5NwMAUC4wkgUA8Ght27YtNmBJ0qFDh1S3bl2Hr/Xs2VObN2/W5s2btXHjRn311Ve6/fbb1aVLF23atEmStGbNGkkqFIoefPBB+fr66scff7RvCw8PLxCmGjZsKEk6c+ZMgX2vu+66QrVYLBbVrVtX+/btK/brAQCUb4xkAQA8WtWqVS/bJjk5WSEhIQ5fCw8PLxR4evTooRYtWmjEiBHauHGjTp8+LckYNbuYn5+fIiIilJqaat8WHBxcoI2Pj/H/lZdeZ1VU3aGhoUpOTr7s1wQAKL8YyQIAlHvh4eFKSUlxur2fn5/atGljv44qLCxMknT8+PEC7S5cuKBTp04pIiLCZbWmp6crPDzcZccDAHgeQhYAoNxr0KCBjhw5UmCCiuLk5uZqx44datCggSSpY8eOkqSPPvqoQLsFCxYoNzfX/rorHDt2TPXq1XPZ8QAAnofTBQEA5V7Xrl0VHx+vXbt2qVWrVgVeO3nypDZs2CDJOKXv+PHjev/997Vnzx57qIqNjdUjjzyiSZMm6fz58+rUqZMSExP14osv6rbbblP37t1dUufevXuVnJysbt26ueR4AADPRMgCAJR77du3V+3atbVkyZJCIWvJkiVasmSJJGPiiWrVqqlVq1b69NNPC9y4+P3331dsbKxmz56tV199VbVr19YzzzyjcePGXXbiDWd98803ql27tm655RaXHA8A4JksNmfPrQAAwIO98cYbmjlzpn7//XeXhSJXa9mypYYNG6ann37a7FIAAGWIa7IAAF5h2LBhstls+uKLL8wuxaFPP/1UFy5c0LBhw8wuBQBQxhjJAgB4jfXr12vAgAHauXOnAgICzC7HLisrSy1bttSHH36om266yexyAABljJAFAAAAAC7E6YIAAAAA4EKELAAAAABwIUIWAAAAALgQIQsAAAAAXIiQBQAAAAAuRMgCAAAAABciZAEAAACACxGyAAAAAMCF/j/ZRTD8s3HJ6gAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# 生成网格\n", "r, w = radial_grid_linear(n=1000, rmin=1e-5, rmax=50.0)\n", "\n", "# 氢原子势 (Z=1)\n", "Z = 1\n", "V_H = -Z / np.maximum(r, 1e-12) # 防止除零\n", "\n", "# 可视化势函数\n", "plt.figure(figsize=(10, 5))\n", "plt.plot(r[:200], V_H[:200], \"b-\", linewidth=2)\n", "plt.axhline(y=0, color=\"k\", linestyle=\"--\", alpha=0.3)\n", "plt.xlabel(\"r (Bohr)\", fontsize=12)\n", "plt.ylabel(\"V(r) (Hartree)\", fontsize=12)\n", "plt.title(\"氢原子库仑势\", fontsize=14)\n", "plt.grid(alpha=0.3)\n", "plt.xlim(0, 10)\n", "plt.ylim(-1.5, 0.2)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 求解氢原子轨道\n", "\n", "使用 FD2 和 FD5 方法分别求解 1s, 2s, 2p 轨道:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "execution": { "iopub.execute_input": "2025-12-04T04:13:16.914471Z", "iopub.status.busy": "2025-12-04T04:13:16.914349Z", "iopub.status.idle": "2025-12-04T04:13:17.336991Z", "shell.execute_reply": "2025-12-04T04:13:17.336885Z" } }, "outputs": [], "source": [ "# 定义要求解的轨道\n", "orbitals = [\n", " {\"n\": 1, \"l\": 0, \"label\": \"1s\", \"n_idx\": 0},\n", " {\"n\": 2, \"l\": 0, \"label\": \"2s\", \"n_idx\": 1},\n", " {\"n\": 2, \"l\": 1, \"label\": \"2p\", \"n_idx\": 0},\n", "]\n", "\n", "results_fd = []\n", "results_fd5 = []\n", "\n", "print(\"氢原子轨道能量对比:\\n\")\n", "print(\"轨道 | 解析解 (Ha) | FD2 (Ha) | FD2 误差 | FD5 (Ha) | FD5 误差\")\n", "print(\"-\" * 75)\n", "\n", "for orb in orbitals:\n", " n, l = orb[\"n\"], orb[\"l\"]\n", " label = orb[\"label\"]\n", " n_idx = orb[\"n_idx\"] # 该 l 通道中的索引\n", " \n", " # 解析解\n", " E_exact = -Z**2 / (2 * n**2)\n", " \n", " # 求解需要的本征态数量(至少要包含该轨道)\n", " k_states = n_idx + 1\n", " \n", " # FD2 求解(二阶精度)\n", " # 注意:solve_bound_states_fd 返回 (k_states, n_points) 形状的数组\n", " eps_fd, u_fd = solve_bound_states_fd(r, l, V_H, k_states)\n", " E_fd = eps_fd[n_idx]\n", " u_fd_orb = u_fd[n_idx, :] # 提取第 n_idx 行(对应该本征态的波函数)\n", " error_fd = abs(E_fd - E_exact) / abs(E_exact)\n", " \n", " # FD5 求解(四阶精度,需要等距网格)\n", " eps_fd5, u_fd5 = solve_bound_states_fd5(r, l, V_H, k_states)\n", " E_fd5 = eps_fd5[n_idx]\n", " u_fd5_orb = u_fd5[n_idx, :] # 提取第 n_idx 行\n", " error_fd5 = abs(E_fd5 - E_exact) / abs(E_exact)\n", " \n", " # 保存结果\n", " results_fd.append({\"label\": label, \"n\": n, \"l\": l, \"energy\": E_fd, \"wavefunction\": u_fd_orb})\n", " results_fd5.append({\"label\": label, \"n\": n, \"l\": l, \"energy\": E_fd5, \"wavefunction\": u_fd5_orb})\n", " \n", " print(f\"{label:4s} | {E_exact:11.8f} | {E_fd:8.6f} | {error_fd:8.2e} | {E_fd5:8.6f} | {error_fd5:8.2e}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 波函数可视化\n", "\n", "绘制径向波函数并检查节点结构:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "execution": { "iopub.execute_input": "2025-12-04T04:13:17.343343Z", "iopub.status.busy": "2025-12-04T04:13:17.343250Z", "iopub.status.idle": "2025-12-04T04:13:17.595770Z", "shell.execute_reply": "2025-12-04T04:13:17.595661Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(1, 3, figsize=(15, 5))\n", "\n", "for i, (ax, res_fd, res_fd5) in enumerate(zip(axes, results_fd, results_fd5)):\n", " label = res_fd[\"label\"]\n", " u_fd = res_fd[\"wavefunction\"]\n", " u_fd5 = res_fd5[\"wavefunction\"]\n", " E_fd = res_fd[\"energy\"]\n", " E_fd5 = res_fd5[\"energy\"]\n", " \n", " # 氢原子解析解(归一化)\n", " if label == \"1s\":\n", " u_exact = 2 * Z**1.5 * r * np.exp(-Z * r)\n", " elif label == \"2s\":\n", " u_exact = (Z / 2)**1.5 / np.sqrt(2) * r * (2 - Z * r) * np.exp(-Z * r / 2)\n", " elif label == \"2p\":\n", " u_exact = (Z / 2)**1.5 / np.sqrt(24) * (Z * r)**2 * np.exp(-Z * r / 2)\n", " \n", " # 归一化解析解\n", " norm_exact = np.sqrt(np.sum(u_exact**2 * w))\n", " u_exact /= norm_exact\n", " \n", " # 调整符号使其一致\n", " if np.sum(u_fd * u_exact) < 0:\n", " u_fd = -u_fd\n", " if np.sum(u_fd5 * u_exact) < 0:\n", " u_fd5 = -u_fd5\n", " \n", " # 绘图\n", " ax.plot(r, u_exact, \"k--\", linewidth=2, label=\"解析解\", alpha=0.7)\n", " ax.plot(r, u_fd, \"b-\", linewidth=1.5, label=\"FD2\", alpha=0.7)\n", " ax.plot(r, u_fd5, \"r-\", linewidth=1.5, label=\"FD5\", alpha=0.7)\n", " ax.axhline(y=0, color=\"k\", linestyle=\"-\", linewidth=0.5, alpha=0.3)\n", " \n", " ax.set_xlabel(\"r (Bohr)\", fontsize=11)\n", " ax.set_ylabel(\"u(r)\", fontsize=11)\n", " ax.set_title(f\"{label} 轨道 (E = {E_fd5:.6f} Ha)\", fontsize=12)\n", " ax.grid(alpha=0.3)\n", " ax.set_xlim(0, 20 if label == \"1s\" else 30)\n", " ax.legend()\n", "\n", "plt.tight_layout()\n", "plt.show()\n", "\n", "print(\"\\n节点规律(节点数 = n - l - 1):\")\n", "for res in results_fd:\n", " u = res[\"wavefunction\"]\n", " nodes = np.sum(np.diff(np.sign(u)) != 0) // 2\n", " expected_nodes = res[\"n\"] - res[\"l\"] - 1\n", " print(f\" {res['label']}: {nodes} 个节点(理论: {expected_nodes})\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 归一化检验\n", "\n", "验证波函数满足归一化条件 $\\int_0^\\infty u^2(r) dr = 1$:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "execution": { "iopub.execute_input": "2025-12-04T04:13:17.601300Z", "iopub.status.busy": "2025-12-04T04:13:17.601193Z", "iopub.status.idle": "2025-12-04T04:13:17.606797Z", "shell.execute_reply": "2025-12-04T04:13:17.606711Z" } }, "outputs": [], "source": [ "print(\"归一化检验:\\n\")\n", "for res_fd, res_fd5 in zip(results_fd, results_fd5):\n", " label = res_fd[\"label\"]\n", " u_fd = res_fd[\"wavefunction\"]\n", " u_fd5 = res_fd5[\"wavefunction\"]\n", " \n", " norm_fd = np.sum(u_fd**2 * w)\n", " norm_fd5 = np.sum(u_fd5**2 * w)\n", " \n", " print(f\"{label} 轨道:\")\n", " print(f\" FD2: ∫u² dr = {norm_fd:.8f}\")\n", " print(f\" FD5: ∫u² dr = {norm_fd5:.8f}\")\n", " print(f\" 数组形状: {u_fd.shape}\")\n", " print()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 精度分析\n", "\n", "### FD2 vs FD5 精度对比\n", "\n", "- **FD2**:O(h²) 截断误差,三对角矩阵\n", "- **FD5**:O(h⁴) 截断误差,五对角矩阵,需要等距网格\n", "\n", "网格加密可显著提升精度,但 FD5 在相同网格下精度更高。\n", "\n", "## 关键概念\n", "\n", "- **本征值问题**:Hamiltonian 矩阵对角化得到能级和波函数\n", "- **边界条件**:$u(0) = 0$,$u(\\infty) = 0$(束缚态)\n", "- **节点定理**:节点数 = n - l - 1\n", "- **归一化**:$\\int_0^\\infty u^2(r) dr = 1$\n", "\n", "## 下一步\n", "\n", "在 **[03-scf.ipynb](03-scf.ipynb)** 中,将这些求解器整合到自洽迭代流程中处理多电子体系。" ] } ], "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": "3.12.2" } }, "nbformat": 4, "nbformat_minor": 4 }