{ "metadata": { "name": "", "signature": "sha256:585bc5ba240dd7c531cf3f17610b32899d911067bd164b9bf50f84748718be3c" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline\n", "from pylab import *\n", "from numpy import *" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "#physical constants\n", "hbar = 1.0\n", "m = 1.0" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "code", "collapsed": false, "input": [ "#discretization\n", "nx = 100\n", "\n", "minx = -1.\n", "maxx = 1.\n", "\n", "x = linspace(minx, maxx, nx)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "#assemble the matrix Hamiltonian\n", "from d2matrix import d2matrix\n", "from scipy.sparse import dia_matrix\n", "\n", "def make_H(V):\n", " nx = len(V)\n", " kinetic = -hbar**2/(2*m)*d2matrix(nx)\n", " potential = diag(V)\n", " H = kinetic + potential\n", " return H\n", "\n", "\n", "V = zeros(nx)\n", "\n", "H = make_H(V)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stderr", "text": [ "/usr/local/lib/python3.4/dist-packages/numpy/core/fromnumeric.py:2507: VisibleDeprecationWarning: rank is deprecated; use the ndim attribute or function instead. To find the rank of a matrix see numpy.linalg.matrix_rank.\n", " VisibleDeprecationWarning)\n" ] } ], "prompt_number": 4 }, { "cell_type": "code", "collapsed": false, "input": [ "# calculate the eigenvectors\n", "eigvals, eigvecs = linalg.eig(H)\n", "eigvecs = array(eigvecs)\n" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 5 }, { "cell_type": "code", "collapsed": false, "input": [ "for i in arange(nx):\n", " plot(x, eigvecs[:,i]+eigvals[i]*150)\n", "ylim([0, 10])" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 6, "text": [ "(0, 10)" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAXMAAAEACAYAAABBDJb9AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ncw8PD48NgCdzDw8Pjw3A/wNMgmjLj4yR1gAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 6 }, { "cell_type": "code", "collapsed": false, "input": [ "def solve(H):\n", " eigvals, eigvecs = linalg.eig(H)\n", " \n", " I = eigvals.argsort()\n", " eigvals = eigvals[I]\n", " eigvecs = array(eigvecs)[:,I]\n", " return eigvals, eigvecs" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 7 }, { "cell_type": "code", "collapsed": false, "input": [ "V = x**2\n", "H = make_H(V)\n", "eigvals, eigvecs = solve(H)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 8 }, { "cell_type": "code", "collapsed": false, "input": [ "figure(figsize(5,6))\n", "for i in arange(10):\n", " plot(x, eigvecs[:,i]*.05+eigvals[i])\n", "plot(x, V, lw=3)\n", "ylim([0, 0.3])" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 9, "text": [ "(0, 0.3)" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAUUAAAFwCAYAAAAvw2lDAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nCoXCCSWKCoVC4YQSRYVCoXDi/wPXeAazDKgrIgAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Two atoms:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#discretization\n", "nx = 100\n", "\n", "minx = -1.\n", "maxx = 1.\n", "\n", "x = linspace(minx, maxx, nx)\n", "\n", "V = zeros(nx)\n", "a1 = -0.5\n", "a2 = 0.5\n", "asize = 0.2\n", "apot = -0.07\n", "V[(x>a1-asize) & (xa2-asize) & (x" ] } ], "prompt_number": 12 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Evolution of a localized electron? Evolution of each eigenvector follows from Schrodinger equation\n", "$$\n", "i\\hbar\\frac{\\partial\\psi_j}{\\partial t} = \\hat H\\psi_j = E_j\\psi_j\n", "$$\n", "$$\n", "\\psi_j(t) = e^{{E_j t}/{i \\hbar}}\\psi_j(0)\n", "$$\n", "And for general initial state\n", "$$\n", "\\psi(0) = \\sum_j c_j\\psi_j(0), {\\rm where }\\quad c_j = \\langle\\psi_j(0)|\\psi(0)\\rangle\n", "$$\n", "is given by\n", "$$\n", "\\psi(t) = \\sum_j c_j\\psi_j(t) = \\sum_j c_j e^{{E_j t}/{i \\hbar}}\\psi_j(0)\n", "$$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "coeffs = zeros(nx)\n", "coeffs[0] = 1/sqrt(2.)\n", "coeffs[1] = 1/sqrt(2.)\n", "E_mean = dot(coeffs*eigvals, coeffs)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 15 }, { "cell_type": "code", "collapsed": false, "input": [ "def psi_t(eigvecs, eigvals, coeffs, t):\n", " phase = exp(eigvals*t/1j*hbar)\n", " #print phase\n", " \n", " psi = zeros(len(coeffs), dtype=complex)\n", " for i in arange(len(coeffs)):\n", " if coeffs[i] != 0.:\n", " psi += eigvecs[:,i]*phase[i]\n", " return psi" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 16 }, { "cell_type": "code", "collapsed": false, "input": [ "from matplotlib import animation\n", "from JSAnimation.IPython_display import display_animation" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 17 }, { "cell_type": "code", "collapsed": false, "input": [ "fig = figure()\n", "ax = axes(xlim=(minx,maxx))\n", "line1, = ax.plot([],[],lw=1)\n", "ax.plot(x, V)\n", "\n", "\n", "def animate(data):\n", " line1.set_data(x, abs(psi_t(eigvecs, eigvals, coeffs, 2000000.*data))*.1+E_mean)\n", "\n", " return line1,\n", "\n", "anim = animation.FuncAnimation(fig, animate, frames=arange(20), interval=100)\n", "display_animation(anim, default_mode='loop')" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", "\n", "\n", "
\n", " \n", "
\n", " \n", "
\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
\n", " Once \n", " Loop \n", " Reflect \n", "
\n", "
\n", "\n", "\n", "\n" ], "metadata": {}, "output_type": "pyout", "prompt_number": 18, "text": [ "" ] } ], "prompt_number": 18 }, { "cell_type": "markdown", "metadata": {}, "source": [ "http://www.hep.manchester.ac.uk/u/forshaw/BoseFermi/Double%20Well.html\n" ] }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] } ], "metadata": {} } ] }