{ "cells": [ { "cell_type": "raw", "metadata": {}, "source": [ "This simple Python example integrates the Schrodinger equation with $V(x) = 0$:\n", "\\begin{equation}\n", "\\left\\{-\\frac{d^2}{dx^2} + V(x)\\right\\} \\psi(x) = E\\psi(x)\n", "\\end{equation}\n", "and then plots the real and imaginary parts of the resulting wave function." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "100000\n" ] }, { "data": { "image/png": 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8O5o1bWjggruO10xsbmavk3+sowa/Hf4XX0S4wkMIcEVbuNDufu8EvWQJ8N//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\nsAUATy91i9BkWCbW/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Ok5g+NR23FlulsbFxQdtVUaTIPgxpKwBlAChCQsTYOi7IgsYQkk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\nzPffHz0pEWOu81tvMf/97/L+6afD/snp0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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import math\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "E = 0.5 #Set the energy of the solution\n", "L = 100 #Set the length of the region in which the solution is determined\n", "Dx = 0.001 #Step size for integrating the Schrodinger equation\n", "N = int(L/Dx) # Number of integration steps\n", "print(N)\n", "V = np.zeros((N,)) # set the potential to zero\n", "psi = np.zeros((N,),dtype=np.complex_) # numpy array holding the N values of the wave function\n", "dpsi = np.zeros((N,),dtype=np.complex_) # numpy array holding the N values of the derivative of the wave function\n", "psi[0] = 1.0 # set an initial value of psi\n", "dpsi[0]=E**0.5*1j # set an initial value of dpsi appropriate for a plane wave traveling to \n", " # the right. Be careful to keep the \"j\" out of the exponent!\n", "for n in range(1, N):\n", " dpsi[n] = dpsi[n-1] - Dx*E*psi[n-1]\n", " psi[n] = psi[n-1] + Dx*dpsi[n-1] # Naive 1st order integrator\n", "# psi[n] = psi[n-1] + Dx*dpsi[n] # Leapfrog, 2nd order integrator\n", "n = np.arange(N)\n", "x = Dx*n\n", "fig=plt.figure(figsize = (10,4)) # define figure of size 10 in x 4 in \n", "ax = fig.add_subplot(1,1,1) # add subfigure #1 in the first row and first column with \"fig\"\n", "ax.plot(x,psi.real,'r-',x,psi.imag,'b--') # determine what is shown in ax. Choose the first \n", " # curve blue solid and the second red dashed.\n", "\n", "ax.set(xlabel='position (x)', ylabel='Re(psi(x)) and Im(psi(x))', # add a tile and axis labels.\n", " title='Schrodinger Solution') \n", "ax.grid(which='major') #superimpose a grid\n", "fig.savefig(\"test.png\") # save the figure as a png file.\n", "plt.show() # Plot the figure here." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "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": "3.6.3" } }, "nbformat": 4, "nbformat_minor": 2 }