{ "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": 2, "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": 3, "metadata": {}, "outputs": [], "source": [ "def mL2V(y):\n", " return 1000*np.sin(20*y) * y**4 " ] }, { "cell_type": "code", "execution_count": 4, "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": 6, "metadata": {}, "outputs": [], "source": [ "w, v = eigh_tridiagonal(d, e)" ] }, { "cell_type": "code", "execution_count": 7, "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=15)\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": 8, "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": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, '$mL^2 E/\\\\hbar^2$')" ] }, "execution_count": 9, "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('$mL^2 E/\\hbar^2$')" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "plt.style.use(['science', 'notebook'])" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "x = np.linspace(0, 1, 1000)\n", "y = np.sin(20*x) * x**4 " ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Potential')" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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