{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## An odd potential\n",
    "\n",
    "So far, the perturbing potentials we have applied have had even symmetry: here we will look at a simple potential with odd symmetry.  This is useful to illustrate more features of perturbation theory, and also to help you think about more aspects of quantum mechanics.  \n",
    "\n",
    "We start, as usual, with the basis set, integration routines, and then define a potential."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "//anaconda/lib/python2.7/site-packages/matplotlib/font_manager.py:273: UserWarning: Matplotlib is building the font cache using fc-list. This may take a moment.\n",
      "  warnings.warn('Matplotlib is building the font cache using fc-list. This may take a moment.')\n"
     ]
    }
   ],
   "source": [
    "# Import libraries and set up in-line plotting.\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as pl\n",
    "import numpy as np\n",
    "# This is a new library - linear algebra includes solving for eigenvalues & eigenvectors of matrices\n",
    "import numpy.linalg as la\n",
    "\n",
    "# Define the eigenbasis - normalisation needed elsewhere\n",
    "def square_well_eigenfunctions(n,width,norm,x):\n",
    "    \"\"\"The eigenbasis for a square well, running from 0 to a, sin(n pi x/a)\"\"\"\n",
    "    fac = np.pi*n/width\n",
    "    return norm*np.sin(fac*x)\n",
    "\n",
    "# We will also define the second derivative for kinetic energy (KE)\n",
    "def second_derivative_square_well_eigenfunctions(n,width,norm,x):\n",
    "    \"\"\"The eigenbasis for a square well, running from 0 to a, sin(n pi x/a)\"\"\"\n",
    "    fac = np.pi*n/width\n",
    "    return -fac*fac*norm*np.sin(fac*x)\n",
    "\n",
    "# Define the x-axis\n",
    "width = 1.0\n",
    "num_x_points = 101\n",
    "x = np.linspace(0.0,width,num_x_points)\n",
    "dx = width/(num_x_points - 1)\n",
    "\n",
    "# Integrate the product of two functions over the width of the well\n",
    "# NB this is a VERY simple integration routine: there are much better ways\n",
    "def integrate_functions(function1,function2,dx):\n",
    "    \"\"\"Integrate the product of two functions over defined x range with spacing dx\"\"\"\n",
    "    # We use the NumPy dot function here instead of iterating over array elements\n",
    "    integral = dx*np.dot(function1,function2)\n",
    "    return integral\n",
    "\n",
    "# Now set up the array of basis functions - specify the size of the basis\n",
    "num_basis = 10\n",
    "# These arrays will each hold an array of functions\n",
    "basis_functions_array = np.zeros((num_basis,num_x_points))\n",
    "second_derivative_functions_array = np.zeros((num_basis,num_x_points))\n",
    "\n",
    "# Loop over first num_basis basis states, normalise and create an array\n",
    "# NB the basis_functions_array will start from 0\n",
    "for i in range(num_basis):\n",
    "    n = i+1\n",
    "    # Calculate A = <phi_n|phi_n>\n",
    "    integral = integrate_functions(square_well_eigenfunctions(n,width,1.0,x),square_well_eigenfunctions(n,width,1.0,x),dx)\n",
    "    # Use 1/sqrt{A} as normalisation constant\n",
    "    normalisation = 1.0/np.sqrt(integral)\n",
    "    basis_functions_array[i,:] = square_well_eigenfunctions(n,width,normalisation,x)\n",
    "    second_derivative_functions_array[i,:] = second_derivative_square_well_eigenfunctions(n,width,normalisation,x)\n",
    "    \n",
    "# Define a function to act on a basis function with the potential\n",
    "def add_potential_on_basis(Hphi,V,phi):\n",
    "    for i in range(V.size):\n",
    "        Hphi[i] = Hphi[i] + V[i]*phi[i]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A weak perturbation\n",
    "\n",
    "The potential will be very simple: a triangular shape at the bottom of the square well.  We'll start by making the magnitude of the potential small with respect to the lowest energy (remember that when we use words like \"small\" they have to be defined relative to an appropriate scale - in this case the energies of the unperturbed system)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x102f1d3d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Define the potential in the square well\n",
    "def square_well_potential(x,V,a):\n",
    "    \"\"\"Potential for a particle in a square well, expecting two arrays: x, V(x), and potential height, a\"\"\"\n",
    "    for i in range(x.size):\n",
    "        V[i] = a*(x[i]-width/2.0)\n",
    "    # Plot to ensure that we know what we're getting\n",
    "    pl.plot(x,V)\n",
    "    \n",
    "# Declare space for this potential (diagonal_Potential) and call the routine\n",
    "diagonal_Potential = np.linspace(0.0,width,num_x_points)\n",
    "square_well_potential(x,diagonal_Potential,1.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we will build the matrix elements of the potential and the overall Hamiltonian.  Look carefully at the potential, and ask yourself if the form of the matrix makes sense: how does the symmetry affect the form ? What effect will this have on the energies of the perturbed system ? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Full Hamiltonian\n",
      "   4.935   -0.180   -0.000   -0.014    0.000   -0.004    0.000   -0.002    0.000   -0.001\n",
      "  -0.180   19.739   -0.195   -0.000   -0.018    0.000   -0.006   -0.000   -0.002   -0.000\n",
      "   0.000   -0.195   44.413   -0.199   -0.000   -0.020   -0.000   -0.006    0.000   -0.003\n",
      "  -0.014   -0.000   -0.199   78.957   -0.200   -0.000   -0.021   -0.000   -0.007   -0.000\n",
      "   0.000   -0.018   -0.000   -0.200  123.370   -0.201    0.000   -0.021   -0.000   -0.007\n",
      "  -0.004   -0.000   -0.020   -0.000   -0.201  177.653   -0.201   -0.000   -0.022    0.000\n",
      "   0.000   -0.006   -0.000   -0.021    0.000   -0.201  241.805   -0.202    0.000   -0.022\n",
      "  -0.002   -0.000   -0.006   -0.000   -0.021   -0.000   -0.202  315.827   -0.202    0.000\n",
      "   0.000   -0.002    0.000   -0.007   -0.000   -0.022    0.000   -0.202  399.719   -0.202\n",
      "  -0.001    0.000   -0.003   -0.000   -0.007    0.000   -0.022    0.000   -0.202  493.480\n",
      "Perturbation matrix elements:\n",
      "   0.000   -0.180   -0.000   -0.014   -0.000   -0.004   -0.000   -0.002    0.000   -0.001\n",
      "  -0.180    0.000   -0.195   -0.000   -0.018   -0.000   -0.006    0.000   -0.002   -0.000\n",
      "  -0.000   -0.195    0.000   -0.199   -0.000   -0.020    0.000   -0.006    0.000   -0.003\n",
      "  -0.014    0.000   -0.199    0.000   -0.200   -0.000   -0.021   -0.000   -0.007   -0.000\n",
      "  -0.000   -0.018   -0.000   -0.200    0.000   -0.201    0.000   -0.021    0.000   -0.007\n",
      "  -0.004   -0.000   -0.020   -0.000   -0.201   -0.000   -0.201   -0.000   -0.022    0.000\n",
      "  -0.000   -0.006    0.000   -0.021    0.000   -0.201    0.000   -0.202    0.000   -0.022\n",
      "  -0.002    0.000   -0.006   -0.000   -0.021   -0.000   -0.202    0.000   -0.202    0.000\n",
      "   0.000   -0.002    0.000   -0.007    0.000   -0.022    0.000   -0.202    0.000   -0.202\n",
      "  -0.001   -0.000   -0.003   -0.000   -0.007    0.000   -0.022    0.000   -0.202    0.000\n"
     ]
    }
   ],
   "source": [
    "# Declare space for the matrix elements\n",
    "H_matrix2 = np.eye(num_basis)\n",
    "\n",
    "# Loop over basis functions phi_n (the bra in the matrix element)\n",
    "print \"Full Hamiltonian\"\n",
    "for n in range(num_basis):\n",
    "    # Loop over basis functions phi_m (the ket in the matrix element)\n",
    "    for m in range(num_basis):\n",
    "        # Act with H on phi_m and store in H_phi_m\n",
    "        H_phi_m = -0.5*second_derivative_functions_array[m] \n",
    "        add_potential_on_basis(H_phi_m,diagonal_Potential,basis_functions_array[m])\n",
    "        # Create matrix element by integrating\n",
    "        H_matrix2[m,n] = integrate_functions(basis_functions_array[n],H_phi_m,dx)\n",
    "        # The comma at the end prints without a new line; the %8.3f formats the number\n",
    "        print \"%8.3f\" % H_matrix2[m,n],\n",
    "    # This print puts in a new line when we have finished looping over m\n",
    "    print\n",
    "    \n",
    "print \"Perturbation matrix elements:\"\n",
    "# Output the matrix elements of the potential to see how large the perturbation is\n",
    "# Loop over basis functions phi_n (the bra in the matrix element)\n",
    "for n in range(num_basis):\n",
    "    # Loop over basis functions phi_m (the ket in the matrix element)\n",
    "    for m in range(num_basis):\n",
    "        # Act with H on phi_m and store in H_phi_m\n",
    "        H_phi_m = np.zeros(num_x_points)\n",
    "        add_potential_on_basis(H_phi_m,diagonal_Potential,basis_functions_array[m])\n",
    "        # Create matrix element by integrating\n",
    "        H_mn = integrate_functions(basis_functions_array[n],H_phi_m,dx)\n",
    "        # The comma at the end prints without a new line; the %8.3f formats the number\n",
    "        print \"%8.3f\" % H_mn,\n",
    "    # This print puts in a new line when we have finished looping over m\n",
    "    print\n",
    "    \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we diagonalise, as usual.  Look at the eigenvalues: do you understand why they take these values ? Is this simple, first order perturbation expansion good enough for this problem ? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Eigenvalues and eigenvector coefficients printed roughly\n",
      "[   4.9326   19.7399   44.4136   78.9571  123.3702  177.653   241.8054\n",
      "  315.8274  399.719   493.4807]\n",
      "[  9.9993e-01   1.2165e-02  -3.3858e-05  -1.9471e-04  -6.9229e-07\n",
      "   2.2987e-05  -6.0505e-08   5.2552e-06   1.0167e-08  -1.6928e-06]\n",
      "[  1.2165e-02  -9.9989e-01   7.8840e-03   1.8058e-05   1.7738e-04\n",
      "  -5.2925e-07   2.5236e-05  -5.7217e-08  -6.4761e-06   1.6305e-08]\n",
      "[  6.0935e-05  -7.8838e-03  -9.9995e-01  -5.7465e-03  -1.0818e-05\n",
      "   1.5022e-04  -3.8187e-07   2.3694e-05   4.6815e-08  -6.5389e-06]\n",
      "\n",
      "    Diag  Perf Square  Difference\n",
      "   4.933        4.935      -0.002\n",
      "  19.740       19.739       0.001\n",
      "  44.414       44.413       0.000\n",
      "  78.957       78.957       0.000\n",
      " 123.370      123.370       0.000\n",
      " 177.653      177.653       0.000\n",
      " 241.805      241.805       0.000\n",
      " 315.827      315.827       0.000\n",
      " 399.719      399.719       0.000\n",
      " 493.481      493.480       0.000\n"
     ]
    }
   ],
   "source": [
    "# Solve using linalg module of numpy (which we've imported as la above)\n",
    "eigenvalues, eigenvectors = la.eigh(H_matrix2)\n",
    "# This call above does the entire solution for the eigenvalues and eigenvectors !\n",
    "# Print results roughly, though apply precision of 4 to the printing\n",
    "print\n",
    "print \"Eigenvalues and eigenvector coefficients printed roughly\"\n",
    "np.set_printoptions(precision=4)\n",
    "print eigenvalues\n",
    "print eigenvectors[0]\n",
    "print eigenvectors[1]\n",
    "print eigenvectors[2]\n",
    "print\n",
    "\n",
    "print \"    Diag  Perf Square  Difference\"\n",
    "for i in range(num_basis):\n",
    "    n = i+1\n",
    "    print \"%8.3f     %8.3f    %8.3f\" % (eigenvalues[i],n*n*np.pi*np.pi/2.0,eigenvalues[i] - n*n*np.pi*np.pi/2.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When we plot the eigenstates, with a small potential it's hard to see the change relative to the unperturbed eigenstates, so we'll also plot the difference between perturbed and unperturbed eigenstates.  What do these differences look like ? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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MerfykF9rNWFxcjLj9+5lzdln09ED8faSknTI8d8XFbJozBbO3BXAY4EBXHut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\nFXkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x102f1de10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Define a figure to take two plots\n",
    "fig = pl.figure(figsize=[12,3])\n",
    "# Add subplots: number in y, x, index number\n",
    "ax = fig.add_subplot(121,autoscale_on=False,xlim=(0,1),ylim=(-2,2))\n",
    "ax.set_title(\"Eigenvectors for changed system\")\n",
    "ax2 = fig.add_subplot(122,autoscale_on=False,xlim=(0,1),ylim=(-0.05,0.05))\n",
    "ax2.set_title(\"Difference to perfect eigenvectors\")\n",
    "for m in range(4): # Plot the first four states\n",
    "    psi = np.zeros(num_x_points)\n",
    "    for i in range(num_basis):\n",
    "        psi = psi+eigenvectors[i,m]*basis_functions_array[i]\n",
    "    if eigenvectors[m,m] < 0:  # This is just to ensure that psi and the basis function have the same phase\n",
    "        psi = -psi\n",
    "    ax.plot(x,psi)\n",
    "    psi = psi - basis_functions_array[m]\n",
    "    ax2.plot(x,psi)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Making the potential larger\n",
    "\n",
    "We will now make the magnitude of the potential larger, so that we're no longer in the weak perturbation regime.  Look at the change to the diagonal of the Hamiltonian, and to the overall eigenvalues.  Are they consistent ? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Full Hamiltonian\n",
      "   4.935   -3.603   -0.000   -0.288    0.000   -0.079    0.000   -0.033    0.000   -0.017\n",
      "  -3.603   19.739   -3.891   -0.000   -0.368    0.000   -0.112   -0.000   -0.049   -0.000\n",
      "  -0.000   -3.891   44.413   -3.970   -0.000   -0.400   -0.000   -0.129    0.000   -0.059\n",
      "  -0.288   -0.000   -3.970   78.957   -4.003   -0.000   -0.417   -0.000   -0.138   -0.000\n",
      "  -0.000   -0.368   -0.000   -4.003  123.370   -4.019    0.000   -0.426   -0.000   -0.144\n",
      "  -0.079   -0.000   -0.400   -0.000   -4.019  177.653   -4.029   -0.000   -0.432    0.000\n",
      "   0.000   -0.112   -0.000   -0.417    0.000   -4.029  241.805   -4.035    0.000   -0.436\n",
      "  -0.033    0.000   -0.129   -0.000   -0.426   -0.000   -4.035  315.827   -4.039    0.000\n",
      "   0.000   -0.049    0.000   -0.138   -0.000   -0.432    0.000   -4.039  399.719   -4.042\n",
      "  -0.017   -0.000   -0.059   -0.000   -0.144    0.000   -0.436    0.000   -4.042  493.480\n",
      "Perturbation matrix elements:\n",
      "   0.000   -3.603   -0.000   -0.288   -0.000   -0.079   -0.000   -0.033    0.000   -0.017\n",
      "  -3.603    0.000   -3.891   -0.000   -0.368   -0.000   -0.112    0.000   -0.049   -0.000\n",
      "   0.000   -3.891    0.000   -3.970   -0.000   -0.400    0.000   -0.129    0.000   -0.059\n",
      "  -0.288   -0.000   -3.970   -0.000   -4.003   -0.000   -0.417   -0.000   -0.138   -0.000\n",
      "  -0.000   -0.368   -0.000   -4.003    0.000   -4.019    0.000   -0.426    0.000   -0.144\n",
      "  -0.079   -0.000   -0.400   -0.000   -4.019   -0.000   -4.029   -0.000   -0.432    0.000\n",
      "  -0.000   -0.112    0.000   -0.417    0.000   -4.029    0.000   -4.035    0.000   -0.436\n",
      "  -0.033    0.000   -0.129   -0.000   -0.426   -0.000   -4.035    0.000   -4.039    0.000\n",
      "   0.000   -0.049    0.000   -0.138    0.000   -0.432    0.000   -4.039    0.000   -4.042\n",
      "  -0.017   -0.000   -0.059   -0.000   -0.144    0.000   -0.436    0.000   -4.042    0.000\n"
     ]
    },
    {
     "data": {
      "image/png": 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kiPhm4jGmkudYhKTXjj9+raRvRcT3Eo4xiYh4TNL/bPGQuebNVBP/VZJeyNx/UZdPZtOP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\ngI5h4geAjmHiB4COYeIHgI75f7QpvzwhqDRWAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10bcf6c10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "diagonal_Potential2 = np.linspace(0.0,width,num_x_points)\n",
    "square_well_potential(x,diagonal_Potential2,20.0)\n",
    "# Declare space for the matrix elements\n",
    "H_matrix3 = np.eye(num_basis)\n",
    "\n",
    "# Loop over basis functions phi_n (the bra in the matrix element)\n",
    "print \"Full Hamiltonian\"\n",
    "for n in range(num_basis):\n",
    "    # Loop over basis functions phi_m (the ket in the matrix element)\n",
    "    for m in range(num_basis):\n",
    "        # Act with H on phi_m and store in H_phi_m\n",
    "        H_phi_m = -0.5*second_derivative_functions_array[m] \n",
    "        add_potential_on_basis(H_phi_m,diagonal_Potential2,basis_functions_array[m])\n",
    "        # Create matrix element by integrating\n",
    "        H_matrix3[m,n] = integrate_functions(basis_functions_array[n],H_phi_m,dx)\n",
    "        # The comma at the end prints without a new line; the %8.3f formats the number\n",
    "        print \"%8.3f\" % H_matrix3[m,n],\n",
    "    # This print puts in a new line when we have finished looping over m\n",
    "    print\n",
    "    \n",
    "print \"Perturbation matrix elements:\"\n",
    "# Output the matrix elements of the potential to see how large the perturbation is\n",
    "# Loop over basis functions phi_n (the bra in the matrix element)\n",
    "for n in range(num_basis):\n",
    "    # Loop over basis functions phi_m (the ket in the matrix element)\n",
    "    for m in range(num_basis):\n",
    "        # Act with H on phi_m and store in H_phi_m\n",
    "        H_phi_m = np.zeros(num_x_points)\n",
    "        add_potential_on_basis(H_phi_m,diagonal_Potential2,basis_functions_array[m])\n",
    "        # Create matrix element by integrating\n",
    "        H_mn = integrate_functions(basis_functions_array[n],H_phi_m,dx)\n",
    "        # The comma at the end prints without a new line; the %8.3f formats the number\n",
    "        print \"%8.3f\" % H_mn,\n",
    "    # This print puts in a new line when we have finished looping over m\n",
    "    print"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Eigenvalues and eigenvector coefficients printed roughly\n",
      "[   4.0834   19.9755   44.5683   79.0523  123.4335  177.6979  241.8388\n",
      "  315.8539  399.7402  493.6551]\n",
      "[  9.7302e-01   2.3030e-01  -1.3321e-02  -4.2000e-03   2.8058e-04\n",
      "   4.6696e-04  -2.4300e-05   1.0562e-04  -4.0734e-06   3.3954e-05]\n",
      "[  2.2955e-01  -9.6072e-01   1.5575e-01   7.1874e-03  -3.6951e-03\n",
      "  -2.1336e-04   5.0959e-04  -2.2948e-05   1.2990e-04  -6.5208e-06]\n",
      "[  2.2642e-02  -1.5451e-01  -9.8109e-01  -1.1424e-01   4.3154e-03\n",
      "   3.0819e-03  -1.5354e-04   4.7700e-04  -1.8763e-05   1.3122e-04]\n",
      "\n",
      "    Diag  Perf Square  Difference\n",
      "   4.083        4.935      -0.851\n",
      "  19.976       19.739       0.236\n",
      "  44.568       44.413       0.155\n",
      "  79.052       78.957       0.095\n",
      " 123.434      123.370       0.063\n",
      " 177.698      177.653       0.045\n",
      " 241.839      241.805       0.033\n",
      " 315.854      315.827       0.027\n",
      " 399.740      399.719       0.021\n",
      " 493.655      493.480       0.175\n"
     ]
    }
   ],
   "source": [
    "# Solve using linalg module of numpy (which we've imported as la above)\n",
    "eigenvalues, eigenvectors = la.eigh(H_matrix3)\n",
    "# This call above does the entire solution for the eigenvalues and eigenvectors !\n",
    "# Print results roughly, though apply precision of 4 to the printing\n",
    "print\n",
    "print \"Eigenvalues and eigenvector coefficients printed roughly\"\n",
    "np.set_printoptions(precision=4)\n",
    "print eigenvalues\n",
    "print eigenvectors[0]\n",
    "print eigenvectors[1]\n",
    "print eigenvectors[2]\n",
    "print\n",
    "\n",
    "print \"    Diag  Perf Square  Difference\"\n",
    "for i in range(num_basis):\n",
    "    n = i+1\n",
    "    print \"%8.3f     %8.3f    %8.3f\" % (eigenvalues[i],n*n*np.pi*np.pi/2.0,eigenvalues[i] - n*n*np.pi*np.pi/2.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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YP0VEuu5DJjn2Sr5DXwAQoRzPQtxrPKp1GD2RimIN+xVsLdUC+IWI1pey3XrciTadTUT+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\nAAAYAgzEVS7tJaO6AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10bd1b6d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Define a figure to take two plots\n",
    "fig = pl.figure(figsize=[12,3])\n",
    "# Add subplots: number in y, x, index number\n",
    "ax = fig.add_subplot(121,autoscale_on=False,xlim=(0,1),ylim=(-2,2))\n",
    "ax.set_title(\"Eigenvectors for changed system\")\n",
    "ax2 = fig.add_subplot(122,autoscale_on=False,xlim=(0,1),ylim=(-1,1))\n",
    "ax2.set_title(\"Difference to perfect eigenvectors\")\n",
    "for m in range(4): # Plot the first four states\n",
    "    psi = np.zeros(num_x_points)\n",
    "    for i in range(num_basis):\n",
    "        psi = psi+eigenvectors[i,m]*basis_functions_array[i]\n",
    "    if eigenvectors[m,m] < 0:  # This is just to ensure that psi and the basis function have the same phase\n",
    "        psi = -psi\n",
    "    ax.plot(x,psi)\n",
    "    psi = psi - basis_functions_array[m]\n",
    "    ax2.plot(x,psi)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "So for this problem first order perturbation theory is not good enough.  We could use higher order perturbation theory here, or a different approach.  We will return to this problem in a notebook on the variational theorem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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