{ "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": 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RlmvhYN9BHO0/Ksai/whGciMIsY25ikxivgSawn1u+hy+nfoWZ6fP\n4sLMBfTF+x4xjEN9h9AV7Vrvyw1oPik0J1fz+l3u4tjAMRztPyrawNENIfAVs4Lz0+dxdvoszk6f\nxbdT32KyMonnep/D0f6jONx/GIf7DmNfz75VFe2npfmk0ByDs9NncWXuCraltrXGYeAoDvUdanuB\n55zjQfmBmAdTZ4Ox0GQtsKfD/YdxpP8INiU2tZVNzdZmcWHmAs7P+DY0dRYLjQUR5PQfw9EBcf07\nczvbXuBNx4SmaO0n5of+90M43Ccm4oFe4cXXSxSrZhVX56/i4sxFXJwV7dLsJfTF+3Ck/wiO9h/F\nsYFjONJ/BGktvS7XuBw455iqTgVOqWnULndxqO8QDvUewqG+Q9jfIyLa9Vge4JxjojKBK3NXcGHm\nAi7OXsSFmQt4WHkYCHdzHPZ079mQ69S2a+Pa/DWcmTrziMBvTW0NxuFg30Hs79m/bqKo27p4wvDH\n4cLsBVyYufCIcDcFsD/Rv+bXtxIU9ALOTonA4NzMuUDgD/YdDMbgYO9B7Ones26OdrY2Gzxtn585\nj/PT53GncAf6/6S3n5h/NfEVzs+cx4WZC7gydwVX5q5AkzXs7tqNndmdGMmNYDg7jC3JLdic3Ize\neO+SPSfnHAW9gKnqFMZKY7hXvId7xXu4mb+Ja/PXUNAL2N21Gwd7xSAe7DuIQ32HNqRwPymcc0zX\npsWE9duVuSsYK41hW2obdnftxo7sDuzI7sBwZhibk5uxObkZiXBiyb/Tci1MV6cxWZ3EveI93C3c\nxd3i3eDxOBlOYl/3PhzsFf1/sO8gdnft3pDC/aTYro3rC9dxceZiIJ5X565Cd3Ts7d6LkdwIdmR2\nYDg7jO2Z7cHeiyIpS/p9nHNUzAomq5OYKE/gXvEebhdu407hDm4s3MBEZQLDmWHs79mPQ30i4DrY\ndxB98b4VvvP2oqAXRBDhB3QXZi7gVv4WemI92NO9B7tyu7A9sx3bM9sxmB7EQGJgWZuuruditj6L\nifIEJioTuFu4i9uF27iVv4UbCzfEclXvAezv9seh/zD29+xHRIm0n5h/97M553hYeYhb+VvBTd0r\n3sNEZQIT5QmUjBKykSxy0RxykRyS4SQ0WYMma1AlFS534XouXO6iZtVQMSuomBXkG3nM1mcRU2Lo\nT/RjKD2E7ZntGEoPYVfXLuzp2oNt6W1t/4i1VliuFazD3yncwZ3CHdwt3sVkdRIPKw8hMQld0S5k\nIhlktAwS4QRUSUVYCkMOyXA8B7Znw3bFxlXZLKNklLDQWEDZKKM33ouBxACG0kOBoxjJjWBv995V\n3WPYaOQbeVybv4Zb+Vu4WxRO717xHqar05irzyETySAXySGlpZDW0sFGuhySIYdk2J4Ny7VgOiaq\nVhVFvYiiUcRCYwGcc2xJbcGmxCYMZ4YDpz2SG8FIbmTJjqLTcD0X90v3cW3+Gm4XbgdB4FhpDNPV\naeiOjr54X6BHyXASMTUGiUmQQzJCLATLtWA4BgzHQNksI9/II6/nUdSLyEay2JLagi3JLdie2Y6d\n2Z3YmduJXbldGEgMPNZRdMSauemYyOt5FPQC8o08qlYVhmNAt3VYrgUpJEFiEqSQhLgaRzKcRCqc\nQiaSQV+8D5qsrcq9PEtwzgODLBpFFPQCalYNlmvBci3Yrg05JEORhKgk1ATSWhppLY1sJIvuWDc5\nzRXA9VzMN+ZR0AsoGSWUjBJqVk04UteG4zlQJRWqpEKRFCTUBLKRbOAAkuFkW61rb1R0W8dMbQZF\no4iKWUHZKKNu14Og0vVchOVwEHQmw0kRkEZyyEVzS9rj6QgxJwiCeNah1/kJgiCeYUjMCYIgOgAS\nc4IgiA6AxJwgCKIDIDEnCILoAEjMCYIgOgASc4IgiA6AxJwgCKIDIDEnCILoAEjMCYIgOgASc4Ig\niA6AxJwgCKID6Nwi0m2EZ3owJ02YEybMhybMKRP2vA1rzoI9b8MpO3ArLpyyA0/34FkeuMXBHQ6E\nACYxsBBDKBJCKBqCFJUgJSUoWQVyVobSpUDtUxHuD0PtVxHeGoa2TYMUkdb71jsKV3dhPDBgPjRh\nTVkwJ01YsxacvAM7b8Mu2HBrbtC4xcFdfxwBMJmBKQwhJYRQLAQ5IUNKSJAzMpRuRYxjj4rwpjDU\nTSrCm8PQtmgIhSnmWkmcmgPzgQlj3IA1bcGaEc2et2EXbThFR8zFhgdP9+DqLuCKiqIAxFwMhxDS\nRJOSEuSULFpOhtqritavIrwlDG2rBnVARUhe3XGkqokrhGd60O/qaNxsoHGzAf2WDv2eDuOeAWvW\ngtqvQtuiIbxFCK7aqwYTWE4LQ5ASEqSoBKYyhNQQIAHgADyAuxye4cFtuPDqHpyKA6fgwC7YwjHM\nWLCmLZhTJsxxE8aEATktIzIUQWRHBJGdokV3RxEdiUKKkdA/DrfhPjqGt3Xod3ToYzqckhOMYXhT\nGOqAP45dCpSccKxSQoIUlyDFJITUEJjMxDgC4A4Htzm4xeHWfdGvurCLYgybDt6atFrOf8qE2qNC\nG9IQGY4gMhJBdFdUfN0ZJaH/MzgVB40bDTRuNFpjeEeHfleHZ3jQti0axz4Vap+Yj3JGFi0lQ4pK\nIoCK+OMIAAyAC3iWB88Qza24cEqOcAR5B9asJdqMBXNCOA17zkZ4UxjasD+OO8U4RndHoQ1pjwg9\nlcBdIzzbg35LR/1KXbSrddSv1WHcN6Bt1YRY+pMtMhyBtl1DeHN41b3yd+EehzVjQb/nG/FtHfot\nXRj3HR1Kr4LY3hhi+2OI7RNfo3uikKLPhsi7uovG9UZrDK/U0bjWgDVjQRvWxETbFRVOcEcEke0R\nqP0qWGhta4R7jgfzoQljzBDjeEtH45ZwNsZ9A9o2DdE9UTGOfouOREUw8AzgVJxHxq9+VYynU3Ja\nY7jLH8MdYk4qXcqa13r3bA/GAwPGXUMEfbca0G+K4M+athDZEUF0bxSxfTEM/c1Q+4m5U3c2rDhw\nl0O/p6N+tY7G1UYg3vodHeFt4ZYI7oshuje6oaIkz/FgjBmPGH/9Sh36LR3hLeFHBX5fdEOLg2d7\n0G8vcr5+MydMRHZGgnuN7ositjcGbbu25o53qXiWf2/XFjmkq77ID2stgfftNDIcAZM25oEVru6i\ncaMR3Gez2fM2Ynv98dsfEwHKvhjCW8Jr7niXSvNpsKk1w/9muP3E/BPtE6gDqpgsfsQa3S2iHaV7\n7b3j43BqDoy7hoh2rovHssZ1EfkoPUogarEDvrjtinbsWrRne9Dv6KhfbolD/XIdxriByJCIHKJ7\n/HEcEU8fSqY9jh+zS/YjTx/163U0rjdg3DO+56BiB2KI7IwgpGwM0X5aXMMXPn/8miJhzVpieWZ3\nFLE94kms+eQhJ9Z/+4xzDnvBFmN4s9Gak9caMB+a0LZrwTyM7fPHcWjjOqg/R1sus7i2C+OuIYzp\nZqO1hnVHB7d5axliS/h768lqrwopKS1L8F3dba0nz/jryf7GR/ORxyk70LZriO70hWq33/ZGIcfX\n38DbAddwod/WRSR/vR5MNv2WDqYysZ67PQJtUCwpNTfw1B6xDinFlz6OnHO4NRd23h/HSX8c/aUH\n474BY8yAZ3hCmEYiiI6I8YvtiSEyEulY5/u0ODWnFaz4X/XbYh1ZTsnQhjRog6KFt4aDDXW1X4WS\nU8Ta8TLG0Sk7Ym9gzhZj6CcEGA8MGPcM6Pd0MIm1xtAP/qL7oogMd67z/S5tKeY/9Nl20YZ+V4cx\nZgSbBOaEKSbsrAV71oZneJBSktggTMrBDjILi+wO+B/PHQ5Xd0UmSMMLNiPgAUqPEmxwhPvDCG8T\nmR7aVg3asIbwwMZ5HGs3OOew522xnjumw7hvCLF9KCapvWDDmrfAHQ45LUOKSyKDIy6BKSxo4P7m\noONvDi7KCLHzNpjKoOT8jJ0BP9NjU/gR8VF71bZ40tuIcI/DnPKd4wPhIM1xU2yoT4uvdt4GAChZ\nBVJSbNRLMQkhTWzUsxADQgg2eD3Ln4uVVqZWSAuJ+ditQh0QmR7hzSLboxnYtcuT3nqy4cT8SfAs\nD07ZgVMSBuGZ/g6y6QVCDiZS95q7zlLEF/+MvKxIglg5XF1MZrcqsjfcmgtuc3i2B25zsBALsj5C\naijIBpHiEuScDEmjyLodcHXhXN2qC6/hZ1bpHrjHRcaVx8FkkYnVDLyklAQ5KQsHQOP4RHSkmBME\nQTxr0IHOBEEQzzAk5gRBEB0AiTlBEEQHQGJOEATRASxJzBljWxhjHzPGrjLGrjDG/tuVvjCCIAji\nyVlSNgtjrA9AH+f8AmMsDuAsgL/mnF9f9DOUzUIQBPGUrGk2C+d8hnN+wf++BuA6gIGlfBZBEASx\nfJa9Zs4YGwRwGMDXy/0sgiAIYmksq/iIv8TytwD+hR+hP8K7774bfD86OorR0dHl/DriMXCPi7cq\nGy7cungzz7O8oHY2PIgazEy8ct2slc7CTLyS7dffflbqXjyLeLYXvHnrNlxwk8Mzxdu33OPibWoO\ncRCKIt7GDYXFISihaCh4G5fKXqwOp06dwqlTp5b9OUt+A5QxpgD4ewDvc87/7WP+ndbMl4hTdYIi\nREF9jBkL9px/iMGCONXGKTlwa64Q5biYeKGIeJW6OSmbNWw4F8LePMXIM/3aGVXxGSElJIryZ2Uo\nWQVKtzj1Run1a6JsCiM8IGppKN0KTex1hHsc1qx/0tFk68Qja3aRjRRscXhJ0Ra1cfyaOKGo/6q9\nbyMI+XVVGIJTkbjdso/mYShuwxWnIqV9++hq2YjaJ4pxqQO+nWwJU5G6ZbCmr/MzUfDk/waQ55z/\nd3/mZ0jM/wxu3Q1OIdLv6a3qf/cNGOM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"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": 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usvT/Q0MazD42G188+4VRiuODDh8g7H4YziacLbPcslPLMMhvEJo6G7e9q72V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"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", "
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