{ "cells": [ { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "$%Be sure that this section is identified as \"Markdown\" in the box above$\n", "Compute $|\\psi(t)\\rangle = e^{-iJ_z \\omega t/\\hbar}|\\psi(0)\\rangle$ and evaluate the three components $\\langle\\psi(t)|S_i|\\psi(t)\\rangle$." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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j6U+tVInv0t995w3PnRIzFi8Gdu2yeHH+9luge3egcWMAJ8ffrVsnqEmKjh2B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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "#define the identity and sigma matrices:\n", "I = np.array([[1.0, 0.0],[0.0, 1.0]])\n", "s1 = np.array([[0.0, 1.0],[1.0, 0.0]])\n", "s2 = np.array([[0.0, -1j],[1j, 0.0]])\n", "s3 = np.array([[1.0, 0.0],[0.0, -1.0]])\n", "#specify the number of steps and the time step to display\n", "Nt=2000;\n", "Dt=0.001;\n", "#specify the angular frequency (2*pi/sec) and \n", "#the initial spinor psi0.\n", "w=2*np.pi;\n", "psi0 = np.array([[1.0],[1.0]])/2**0.5\n", "#set up arrays to hold the times and 3 spin expectation values at those times\n", "t = np.zeros((Nt,)) # define the array holding the time (needed for the plot)\n", "S1 = np.zeros((Nt,)) # define the array holding \n", "S2 = np.zeros((Nt,)) # define the array holding \n", "S3 = np.zeros((Nt,)) # define the array holding \n", "#evaluate Nt time steps\n", "for nt in range(1,Nt):\n", " t[nt]=Dt*nt\n", " #calculate the 2x2 rotation matrix for the time step nt\n", " U = np.cos(w*t[nt]/2)*I +1j*np.sin(w*t[nt]/2)*s3\n", " #calculate the rotated spinor at time step nt. \n", " psi = np.dot(U,psi0) # multiply U on psi0 to obtain psi\n", " #use that spinor to compute the matrix elements of\n", " #the three sigma matrices for each time step and\n", " #store the result in an array to be plotted below.\n", " # calculate the expectation value of s1\n", " S1[nt]=np.real(np.dot(np.transpose(np.conjugate(psi)),np.dot(s1,psi))[0][0])\n", " # calculate the expectation value of s2\n", " S2[nt]=np.real(np.dot(np.transpose(np.conjugate(psi)),np.dot(s2,psi))[0][0])\n", " # calculate the expectation value of s3\n", " S3[nt]=np.real(np.dot(np.transpose(np.conjugate(psi)),np.dot(s3,psi))[0][0])\n", "#plot all three spin projections\n", "fig, (ax) = plt.subplots(nrows=1, figsize=(10, 8))\n", "ax.plot(t,S1,'r-',t,S2,'b--',t,S3,'k:')\n", "plt.show()" ] }, { "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 }