Schrodinger-equation/Schrödinger.ipynb
2022-02-09 21:44:01 +08:00

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Plaintext

{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "occupied-banks",
"metadata": {},
"outputs": [],
"source": [
"from scipy import integrate\n",
"import numpy as np\n",
"import math\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "fossil-belief",
"metadata": {},
"outputs": [],
"source": [
"# энергия частицы\n",
"e=1.3\n",
"# константа частицы\n",
"h=0.5\n",
"# фактор потенциальной ямы\n",
"A=1.5\n",
"# константы интегрирования\n",
"a = 0.0\n",
"b = 10.0\n",
"step = 0.005\n",
"# начальные условия\n",
"alpha=0\n",
"beta=1\n",
"# неиспользуемые дополнительные переменные\n",
"omega=1\n",
"phi=0"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "completed-shore",
"metadata": {},
"outputs": [],
"source": [
"def u(x):\n",
" \"\"\"\n",
" Функция потенциала,\n",
" прямоугольная потенциальная яма\n",
" \"\"\"\n",
" if x>5.0:\n",
" return A*1e1\n",
" else:\n",
" return A"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "simple-swiss",
"metadata": {},
"outputs": [],
"source": [
"def se_solve(Y,x):\n",
" \"\"\"\n",
" Функция, задающая систему дифференциальных уравнений\n",
" \"\"\"\n",
" return [Y[1],(e-u(x))/h*Y[0]]"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "celtic-schedule",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x2b5bf3d0>]"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# массивы для решения задачи\n",
"a_x=np.arange(a,b,step)\n",
"y=np.arange(a,b,step)\n",
"# интегрируем систему уравнений\n",
"asol=integrate.odeint(se_solve,[alpha,beta],a_x)\n",
"# на графике будем изображать квадрат модуля волновой функции\n",
"# несущий физический смысл плотности вероятности\n",
"for i in range(0,len(asol)):\n",
" y[i]=asol[i][0]**2\n",
"plt.plot(y)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "checked-arthritis",
"metadata": {},
"outputs": [],
"source": []
}
],
"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": "3.8.2"
}
},
"nbformat": 4,
"nbformat_minor": 5
}