{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.linalg import eigh_tridiagonal" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$ \\begin{bmatrix}\\frac{1}{\\Delta y^2}+mL^2V_1 & -\\frac{1}{2 \\Delta y^2} & 0 & 0...\\\\ -\\frac{1}{2 \\Delta y^2} & \\frac{1}{\\Delta y^2}+mL^2V_2 & -\\frac{1}{2 \\Delta y^2} & 0... \\\\ ...& ... & ... & -\\frac{1}{2 \\Delta y^2}\\\\...0 & 0 & -\\frac{1}{2 \\Delta y^2} & \\frac{1}{\\Delta y^2}+mL^2V_{N-1} \\\\ \\end{bmatrix} \\begin{bmatrix} \\psi_1 \\\\ \\psi_2 \\\\ ... \\\\ \\psi_{N-1} \\end{bmatrix} = mL^2 E \\begin{bmatrix} \\psi_1 \\\\ \\psi_2 \\\\ ... \\\\ \\psi_{N-1} \\end{bmatrix} $$\n", "\n", "$$ \\psi_0 = \\psi_N = 0$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Define what $N$ and $dy$ is" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "N = 100\n", "dy = 1/N\n", "y = np.linspace(0, 1, N+1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Define potential $mL^2 V$" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([1.e+08, 1.e+08, 1.e+08, 1.e+08, 1.e+08, 1.e+08, 1.e+08, 1.e+08,\n", " 1.e+08, 1.e+08, 1.e+08, 1.e+08, 1.e+08, 1.e+08, 1.e+08, 1.e+08,\n", " 1.e+08, 1.e+08, 1.e+08, 1.e+08, 1.e+08, 1.e+08, 1.e+08, 1.e+08,\n", " 1.e+08, 0.e+00, 0.e+00, 0.e+00, 0.e+00, 0.e+00, 0.e+00, 0.e+00,\n", " 0.e+00, 0.e+00, 0.e+00, 0.e+00, 0.e+00, 0.e+00, 0.e+00, 0.e+00,\n", " 0.e+00, 0.e+00, 0.e+00, 0.e+00, 0.e+00, 0.e+00, 0.e+00, 0.e+00,\n", " 0.e+00, 0.e+00, 0.e+00, 0.e+00, 0.e+00, 0.e+00, 0.e+00, 0.e+00,\n", " 0.e+00, 0.e+00, 0.e+00, 0.e+00, 0.e+00, 0.e+00, 0.e+00, 0.e+00,\n", " 0.e+00, 0.e+00, 0.e+00, 0.e+00, 0.e+00, 0.e+00, 0.e+00, 0.e+00,\n", " 0.e+00, 0.e+00, 0.e+00, 0.e+00, 1.e+08, 1.e+08, 1.e+08, 1.e+08,\n", " 1.e+08, 1.e+08, 1.e+08, 1.e+08, 1.e+08, 1.e+08, 1.e+08, 1.e+08,\n", " 1.e+08, 1.e+08, 1.e+08, 1.e+08, 1.e+08, 1.e+08, 1.e+08, 1.e+08,\n", " 1.e+08, 1.e+08, 1.e+08, 1.e+08, 1.e+08])" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.where(((y<0.25) | (y>0.75)), 1e8, 0)" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [], "source": [ "def mL2V(y):\n", " #return 1000*np.sin(20*y) * y**4 \n", " return np.where(((y<0.25) | (y>0.75)), 1e8, 0)" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [], "source": [ "d = 1/dy**2 + mL2V(y)[1:-1]\n", "e = -1/(2*dy**2) * np.ones(len(d)-1)" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [], "source": [ "w, v = eigh_tridiagonal(d, e)" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10,5))\n", "plt.plot(y, mL2V(y), lw=10)\n", "plt.title('Potential', fontsize=30)\n", "plt.ylabel('$V/V_0$', fontsize=25)\n", "plt.xlabel('$x/L$', fontsize=25)\n", "plt.grid()\n", "plt.savefig('v3p1.png', dpi=200)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10,5))\n", "plt.plot(y[1:-1], v.T[0])\n", "plt.plot(y[1:-1], v.T[1])\n", "plt.plot(y[1:-1], v.T[2])\n", "plt.plot(y[1:-1], v.T[3])\n", "plt.title('Eigenstates', fontsize=30)\n", "plt.ylabel('$\\psi$', fontsize=25)\n", "plt.xlabel('$x/L$', fontsize=25)\n", "plt.grid()\n", "plt.savefig('v3p2.png', dpi=200)\n", "\n" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, '$mL^2 E/\\\\hbar^2$')" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.bar(np.arange(0, 10, 1), w[0:10])\n", "plt.ylabel('$mL^2 E/\\hbar^2$', fontsize=20\n", " )" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "#plt.style.use(['science', 'notebook'])" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "x = np.linspace(0, 1, 1000)\n", "y = np.sin(20*x) * x**4 " ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Potential')" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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