Created
December 27, 2021 04:26
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| { | |
| "cells": [ | |
| { | |
| "cell_type": "code", | |
| "execution_count": 1, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "import numpy as np\n", | |
| "import matplotlib.pyplot as plt\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 21, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "def f(x,r2):\n", | |
| " return r2*np.sin(x)/x + np.cos(x)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 45, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "2.46454358134891 3.141592653589793 5.035909176601691 6.283185307179586 7.752104161802669 9.42477796076938\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "def func(x):\n", | |
| " return f(x,7)-1\n", | |
| "def gunc(x):\n", | |
| " return f(x,7)+1\n", | |
| "from scipy import optimize\n", | |
| "s1=optimize.fsolve(func, 2)[0]\n", | |
| "s2=optimize.fsolve(gunc, 2)[0]\n", | |
| "s3=optimize.fsolve(gunc, 6)[0]\n", | |
| "s4=optimize.fsolve(func, 6)[0]\n", | |
| "s5=optimize.fsolve(func, 8)[0]\n", | |
| "s6=optimize.fsolve(gunc, 10)[0]\n", | |
| "print(s1,s2,s3,s4,s5,s6)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 28, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "2.1556155699335577" | |
| ] | |
| }, | |
| "execution_count": 28, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "s2" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 65, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stderr", | |
| "output_type": "stream", | |
| "text": [ | |
| "/home/kawahara/.pyenv/versions/anaconda3-2019.07/lib/python3.7/site-packages/ipykernel_launcher.py:2: RuntimeWarning: invalid value encountered in true_divide\n", | |
| " \n" | |
| ] | |
| }, | |
| { | |
| "data": { | |
| "image/png": 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\n", | |
| "text/plain": [ | |
| "<Figure size 432x288 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": { | |
| "needs_background": "light" | |
| }, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "xarr=np.linspace(0.0,10.0,1000)\n", | |
| "\n", | |
| "plt.figure()\n", | |
| "plt.plot(xarr,f(xarr,7.0),color=\"black\",label=\"$r^2=7$\")\n", | |
| "plt.fill_between([0,10],-1,1,alpha=0.2,color=\"black\")\n", | |
| "plt.fill_between([s1,s2],-2,-1.8,alpha=0.9,color=\"black\")\n", | |
| "plt.fill_between([s3,s4],-2,-1.8,alpha=0.9,color=\"black\")\n", | |
| "plt.fill_between([s5,s6],-2,-1.8,alpha=0.9,color=\"black\")\n", | |
| "plt.xlabel(\"$x=H \\\\sqrt{2 m E}/\\\\hbar$\",fontsize=14)\n", | |
| "plt.ylabel(\"$f(x) = r^2 \\\\sin{x}/x + \\\\cos{x}$\",fontsize=14)\n", | |
| "plt.plot([s1,s2,s3,s4,s5,s6],[1,-1,-1,1,1,-1],\"o\",color=\"black\")\n", | |
| "plt.legend(fontsize=14)\n", | |
| "plt.savefig(\"Kronig_Penney.pdf\", bbox_inches=\"tight\", pad_inches=0.0)\n", | |
| "plt.show()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "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": "3.7.3" | |
| } | |
| }, | |
| "nbformat": 4, | |
| "nbformat_minor": 2 | |
| } |
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