{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## A different basis set\n", "\n", "It is important to understand that a basis set is just a means to an end: we choose it when representing a particular system for convenience, or because of simple mathematical operations, or other reasons. In previous notebooks when looking at the square well, we used a basis set of the simple square well (sine functions) for obvious reasons. In this notebook we will develop an alternative basis set for the square well, and explore its functionality.\n", "\n", "An obvious set of functions to choose are polynomials: the set is easy to extend, and algebraic manipulations are simple. We start with simple definitions." ] }, { "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 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" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now define the basis set. We know that it must go to zero at $x=0$ and $x=a$ (for a well of width $a$). The simplest polynomial that will do this is a quadratic like $x(a-x)$ so we'll start with this. We can then extend the basis by multiplying by extra x terms. How do we define a sensible way to do this ? We'll draw on our knowledge of the system: we know that, with the eigenbasis, each successive basis function adds another node (another point where $\\psi(x) = 0$). We can add this easily by multiplying by $(x-b)$ and choosing the value of $b$ carefully. You can see how I've done this below (if you're not happy with reading python, look at the output where it says \"zero point\").\n", "\n", "There are two more things I've introduced below: a different way of finding the second derivative (a technique known as finite differences); and orthogonalisation. I'll discuss orthogonalisation first.\n", "\n", "It is much easier if a basis set is orthonormal (i.e. $\\langle \\phi_i \\vert \\phi_j \\rangle = \\delta_{ij}$ ). Our polynomial basis set as defined isn't orthogonal (or normalised) so we use a procedure called Gram-Schmidt orthogonalisation to make it well behaved. The idea is very simple: for each basis function, we project out components of previous functions: \n", "\n", "$$\n", "\\vert \\phi_i^\\prime\\rangle = \\vert \\phi_i\\rangle - \\frac{\\langle \\phi_j^\\prime\\vert\\phi_i\\rangle }{\\langle \\phi_j^\\prime\\vert\\phi_j^\\prime\\rangle}\\vert \\phi_j^\\prime \\rangle\n", "$$\n", "\n", "where we perform the operation for $j=1,\\ldots,i-1$ and the new, orthonormalised functions have a prime. (To derive this, start by writing $\\vert \\phi_i^\\prime \\rangle = \\vert \\phi_i \\rangle + \\alpha \\vert \\phi_j^\\prime \\rangle$ and then solve for $\\alpha$ by asserting that $\\langle \\phi_i^\\prime \\vert \\phi_j^\\prime \\rangle = 0$.)\n", "\n", "The finite differences method (which we use in the routine `second_derivative_finite` below) is based on finding a small change in a function coming from a small difference to find its derivative (as in the formal definition of differentiation, but without taking the limit where the difference becomes infinitely small). The second derivative is just found as a small change in the first derivative. While we could calculate the derivative analytically, this is somewhat simpler (and remarkably accurate provided that the number of points we use along the x axis is large enough)." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "n is 0\n", "n is 1\n", "zero point is 0.5\n", "n is 2\n", "zero point is 0.333333333333\n", "zero point is 0.666666666667\n", "n is 3\n", "zero point is 0.25\n", "zero point is 0.5\n", "zero point is 0.75\n", "n is 4\n", "zero point is 0.2\n", "zero point is 0.4\n", "zero point is 0.6\n", "zero point is 0.8\n", "n is 5\n", "zero point is 0.166666666667\n", "zero point is 0.333333333333\n", "zero point is 0.5\n", "zero point is 0.666666666667\n", "zero point is 0.833333333333\n", "n is 6\n", "zero point is 0.142857142857\n", "zero point is 0.285714285714\n", "zero point is 0.428571428571\n", "zero point is 0.571428571429\n", "zero point is 0.714285714286\n", "zero point is 0.857142857143\n", "n is 7\n", "zero point is 0.125\n", "zero point is 0.25\n", "zero point is 0.375\n", "zero point is 0.5\n", "zero point is 0.625\n", "zero point is 0.75\n", "zero point is 0.875\n", "n is 8\n", "zero point is 0.111111111111\n", "zero point is 0.222222222222\n", "zero point is 0.333333333333\n", "zero point is 0.444444444444\n", "zero point is 0.555555555556\n", "zero point is 0.666666666667\n", "zero point is 0.777777777778\n", "zero point is 0.888888888889\n", "n is 9\n", "zero point is 0.1\n", "zero point is 0.2\n", "zero point is 0.3\n", "zero point is 0.4\n", "zero point is 0.5\n", "zero point is 0.6\n", "zero point is 0.7\n", "zero point is 0.8\n", "zero point is 0.9\n", "\n", "Now check that the basis set is orthonormal\n", "\n", " 1.000 -0.000 -0.000 -0.000 0.000 -0.000 -0.000 0.000 0.000 -0.000\n", " -0.000 1.000 0.000 0.000 -0.000 -0.000 0.000 0.000 0.000 -0.000\n", " -0.000 0.000 1.000 -0.000 -0.000 0.000 0.000 0.000 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xiUWIGnx9fQn086HNQznqLNCDLbOhS273ZYEOWBuAfmj3FHUTJkxw6wfdQfKj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\nbbPZ5IhiR2fk00+lgp2WJmX2iSfKJTl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LTXiU+gjxs+MR5hGGzPWZ4D9vgVWAiAnD332X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\nC5yuOU1edR4nq07S0NbAdWnXcV3adfxy1S9ZOH6h3OY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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Test polynomials\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_array = np.zeros((num_basis,num_x_points))\n", "second_derivative_basis_array = np.zeros((num_basis,num_x_points))\n", "\n", "def polynomial(x,n,width):\n", " func = x*(width-x)\n", " print \"n is \",n\n", " for i in range(n):\n", " print \"zero point is \",(i+1.0)/(n+1.0)\n", " func = func*(x-width*((i+1.0)/(n+1.0)))\n", " return func\n", "\n", "def second_derivative_finite(f,dx):\n", " second_derivative = np.zeros(f.size)\n", " for i in range(1,f.size-1):\n", " second_derivative[i] = (f[i+1] + f[i-1] - 2.0*f[i])/(dx*dx)\n", " second_derivative[0] = (f[1]-2.0*f[0])/(dx*dx)\n", " second_derivative[f.size-1] = (f[f.size-2]-2.0*f[f.size-1])/(dx*dx)\n", " return second_derivative\n", " \n", "# 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(\"Basis set before orthonormalisation\")\n", "ax2 = fig.add_subplot(122,autoscale_on=False,xlim=(0,1),ylim=(-2,2))\n", "ax2.set_title(\"Basis set after orthonormalisation\")\n", "\n", "for i in range(num_basis):\n", " basis_array[i,:] = polynomial(x,i,width)\n", " normalisation_factor = integrate_functions(basis_array[i,:],basis_array[i,:],dx)\n", " basis_array[i,:] = basis_array[i,:]/np.sqrt(normalisation_factor)\n", " ax.plot(x,basis_array[i,:])\n", " if i>0:\n", " for j in range(i):\n", " overlap = integrate_functions(basis_array[i,:],basis_array[j,:],dx)\n", " basis_array[i,:] = basis_array[i,:] - overlap*basis_array[j,:]\n", " normalisation_factor = integrate_functions(basis_array[i,:],basis_array[i,:],dx)\n", " basis_array[i,:] = basis_array[i,:]/np.sqrt(normalisation_factor)\n", " second_derivative_basis_array[i,:] = second_derivative_finite(basis_array[i,:],dx)\n", " ax2.plot(x,basis_array[i,:])\n", " \n", "print\n", "print \"Now check that the basis set is orthonormal\"\n", "print\n", "for i in range(num_basis):\n", " for j in range(num_basis):\n", " overlap = integrate_functions(basis_array[i,:],basis_array[j,:],dx)\n", " print \"%8.3f\" % overlap,\n", " print\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Using the basis set\n", "\n", "Now that we have defined our basis, we can use it to build a Hamiltonian and solve the square well problem, in the usual manner. But we will **not** expect the Hamiltonian to be diagonal in this basis. We will then diagonalise the Hamiltonian to find the eigenvalues in this finite basis, and compare them to the exact result. We'll also look at the eigenvectors." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Full Hamiltonian\n", " 5.000 0.000 1.729 -0.000 0.957 -0.000 0.623 -0.000 0.439 -0.000\n", " 0.000 20.990 -0.000 9.915 -0.000 6.047 -0.000 4.121 0.000 2.966\n", " 1.729 0.000 50.928 0.000 28.178 0.000 18.347 0.000 12.913 0.000\n", " -0.000 9.915 0.000 98.688 -0.000 60.189 0.000 41.020 0.000 29.524\n", " 0.957 -0.000 28.178 0.000 167.968 0.000 109.363 0.000 76.974 0.000\n", " 0.000 6.047 0.000 60.189 -0.000 262.161 0.000 178.665 -0.000 128.597\n", " 0.623 0.000 18.347 -0.000 109.363 0.000 384.170 -0.000 270.394 -0.000\n", " -0.000 4.121 0.000 41.020 0.000 178.665 -0.000 536.190 -0.000 385.930\n", " 0.439 0.000 12.913 0.000 76.974 0.000 270.394 -0.000 719.459 0.000\n", " 0.000 2.966 0.000 29.524 0.000 128.597 0.000 385.930 0.000 934.016\n" ] } ], "source": [ "# First let's solve the simple square well\n", "# Declare space for the matrix elements - simplest with the identity function\n", "H_Matrix = np.eye(num_basis)\n", "\n", "# Define a function to act on a basis function with the potential\n", "def Add_Potential_to_basis(Hphi,V,phi):\n", " for i in range(V.size):\n", " Hphi[i] = Hphi[i] + V[i]*phi[i]\n", " \n", "print \"Full Hamiltonian\"\n", "# Loop over basis functions phi_n (the bra in the matrix element)\n", "# Calculate and store the matrix elements for the 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", " # First the kinetic energy\n", " H_phi_m = -0.5*second_derivative_basis_array[m] \n", " # Potential is zero for the pure square well\n", " # Create matrix element by integrating\n", " H_mn = integrate_functions(basis_array[n],H_phi_m,dx)\n", " H_Matrix[m,n] = H_mn\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": 4, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 4.9344 19.7327 44.3804 78.8532 123.2618 177.7711\n", " 264.0253 359.6702 890.9226 1216.0167]\n", "[ 9.9928e-01 -7.5045e-15 -3.7010e-02 -5.4982e-16 8.0193e-03\n", " -3.0331e-16 3.1466e-03 -7.0542e-17 -1.0064e-03 -3.9935e-17]\n", "[ -7.3101e-15 -9.9144e-01 1.5543e-15 1.2393e-01 -1.6653e-16\n", " 3.7062e-02 -2.7756e-16 1.6914e-02 2.7756e-16 5.3650e-03]\n", "[ -3.8006e-02 -8.8818e-16 -9.6852e-01 1.7764e-15 2.2668e-01\n", " 9.7145e-17 9.0925e-02 1.1102e-16 -2.9471e-02 8.9338e-17]\n" ] } ], "source": [ "# Solve using linalg module of numpy (which we've imported as la above)\n", "EigenValues, Eigenvectors = la.eigh(H_Matrix)\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", "np.set_printoptions(precision=4)\n", "print EigenValues\n", "print Eigenvectors[0]\n", "print Eigenvectors[1]\n", "print Eigenvectors[2]" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " Changed Original Difference\n", " 4.934 4.935 -0.000\n", " 19.733 19.739 -0.006\n", " 44.380 44.413 -0.033\n", " 78.853 78.957 -0.104\n", " 123.262 123.370 -0.108\n", " 177.771 177.653 0.118\n", " 264.025 241.805 22.220\n", " 359.670 315.827 43.843\n", " 890.923 399.719 491.204\n", "1216.017 493.480 722.537\n" ] } ], "source": [ "# Now print out eigenvalues and the eigenvalues of the perfect square well, and the difference\n", "print \" Changed Original 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": [ "### Accuracy of a basis\n", "\n", "We have just found that the eigenvalues for the square well using ten polynomials (instead of the eigenbasis) are very accurate for the first few eigenvalues, but then diverge - with errors which are close to 10% for $n=7$, getting larger after that. What is happening ? \n", "\n", "This is (another) sign of a basis set that is finite: the first few eigenvectors are well represented by our ten basis functions, but as we get to higher eigenvectors with higher curvature our first ten basis functions do not describe these functions as well. We can see this by plotting the eigenvectors, and the difference to the perfect eigenvectors, below. You might like to try increasing the basis size, and seeing how the eigenvalues improve. (It is also possible that our finite different approximation is breaking down for the highest eigenvectors - you could try increasing the number of points used along the x axis to test this.)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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PWX6Kj2f8gQP806uXw4WCzhAdDX/8obfff9eu9YYOhWrDjvNdnaNsuKAXTbzh\npEdG6oWB552nbZUr0/3csmVwzz3w4Ydw442VV28JGAXaYDAYqg5GgS4D82JjefrwYdb36uXYbCMi\nQmsq/frpKeky2iTn22xcvmkN+2PWclHGGt4a+CZdmnQpWyOPHoXrroMhQ2D6dI/YeiZnpTDpu9dY\ndOgTGu14jtx1DzF0sC9DhugRUX//Sm9SlWBbWhoDd+xgWdeu9K5f3yVl2mywbRssX663rT0OU+fy\nZKbndWfktb6euxYHDug3qIcegiee8IxN8r//wvDhMGECTJnicbtoo0AbDAZD1cEo0E7yd0oK1+/a\nxf917+7YjjQ8XCvOEybAY4+V+WGcnJ3MlN+n8NOh/6PGBR8xIbQDj5fXY0BCAgweDL17a9MOd9iT\nFqGgANauhe+/1972atWCK0buY0vweHxqpvPJdZ/QM7ic3hTOAY7l5HDx1q282bYtN5UjaI6zHI8V\nhm/ew7EoRcqUTvS+SDFyJIwcWYm25rt2waBB2tPGvfdWUqXFEBWl75VRo7T9tQcxCrTBYDBUHbwl\nlLdXk5yXx6179vBZx47FK8/9+2tPGJMnl1l5/v3Q73T7sBvVfKqxb/xW1lx0GW9ERrIhNbV8DQ4I\n0PP327fDffdp7dYN2GxaaZ44UftafuQRHbdixQrYtw8+efU8tkxcycTeExn09SBe+usl8m35bmlL\nVcYmwp1793JP06ZuVZ4BmgYp/hp8HoEXZPLK9mM8+KC2ST/vPP0X/vBDbUPtNrZu1b6Z33jD88oz\n6D/un39q/+oeVqANBoPBcG5wzoxA375nD42qVeMDRxEAIyL0yHOht40ykJmXydTfp7Jk/xLmDJ/D\nNW2vOXnsuxMnePrIEf698MJS3dsVS0aG9n97/vl6JNpFU9Q7d+q1ivPnaxPv0aO12XfHjsXniUqN\n4t4l95KcncxXN3xFx8ASEp9jvBsVxYITJ1jTo4fz/sAryO6MDK7891/W9+pFu9q1ycqCX3/VZvu/\n/KK9oNx2mzZRdpnjjv379b0yc6Ye8vYmYmP1G8To0fDccx5pghmBNhgMhqqDMeEohQWxsbwQHs6W\nCy44c9FgUpL2H3bvvfD442Uqd0/cHm7+9ma6BXVj5tCZNKrV6Iw0Y/bupbavLx8WE7rbKVJS4Mor\n9RT1f/9b7mJiY2HePJg7V4eovv12vXXt6nwZIsKHmz/k+VXP89bAt7iz+53lbs/Zwp6MDK6wU2Qr\nk3ciI1nUiCufAAAgAElEQVQUF8fqIop7RgYsXapfktat02bCd92l9cty6/fR0fpeef55vXjPGzl+\nXN8rkybBf/5T6dUbBdpgMBiqDkaBLoHI7Gwu2LKF5V27cmHRRV05OdqOs2dPePvtMpU7d/tcJv82\nmelXT+eeHvcUG2o5JT+f7ps2MbNDB4YFBJS3G1ox6NtXe+cYO9bpbHl5euHZZ59p7xkjRsCYMXoQ\nsSIDpTtid3DztzfTt0Vf3h/6PrWrV67i6C3k2mz02bqV/4SE8EBISKXXbxNh4Pbt9G/UiGdCQx2m\niY3VMw1ffql9dt99t97K5G48KUn7KLzjDv0f9GYOHdLRaT75BK69tlKrNgq0wWAwVB0qJLNFpMIb\nMAeIBXaUkOY9IAzYBvQoIZ24CpvNJkO2b5cXjxw582BBgchtt4mMHCmSn+90mTn5OTLup3Fy3gfn\nyY7jO5zK81dSkoSsWyfJeXlO1+OQsDCR4GCR5ctLTXrwoMiTT4o0bSpy2WUic+aIpKZWrPqipOWk\nye3f3y5dZ3WVw4mHXVt4FWHakSMybPt2sdlsHmtDZFaWBK5dK7vS00tNu3WryMSJIoGBIldfLbJw\noUhOTimZcnNF+vUTmTRJxIP9LBPr1+tObtpUqdVa8sslcrXoBgwG9gEHgKnFpHEoZ4vLC9wI7AIK\ngF5FynrKKmsvMLCEdrntfBoMBoM7qYjMdpVgvwzoUZwCDQwBfra+XwysL6Esl52YH0+ckE4bNkhO\nQcGZB597TqRPH5HMTKfLO5Z2TPrO6Ssj5o+Q1OyyaaP37d0rk8LCypTHIWvXijRuLLJ//xmHcnNF\nvvtOZMAAnWTyZJG9eyteZUnYbDZ5b/17EjQjSP449Id7K/MyDmVmSsCaNRKeleXppsj7kZHS799/\nnVbks7JE5s0T6d9fpEkTkSlTRA4dKibxhAkiQ4eW6UXTK1i8WCQkRCQystKqdJcCjV7wfRAIBapb\nCvJ54oScLSkv0BFoD/xpr0ADnYB/gWpAKyu/KqZtbj6rBoPB4B4qIrNdstpJRNYCSSUkGQHMtdJu\nABoopdwagzezoIBJBw/yQfv2+BW1VVi6VNs0FPpqc4ItMVvo/UlvrmlzDT/c8gP1ajgfXAXg1TZt\n+CY2lp3p6WXKdwZ9+8LLL2tbjJQUAI4d04HZWrXSrqvvvVfHt3jjDe2ZwZ0opZh48UTmj5rP7T/c\nznsb3it8qJ71TDp4kMktWpQ7WIorGR8SQlJeHgtPnHAqfc2aOl7Pn39qLywFBTogztChOmCOzWYl\nnDNHR3KZN89hGHuvZsQI7V7mxhu1uVbVpjcQJiLhIpIHLEDLVXuKk7PF5hWR/SISBhSdwhwBLBCR\nfBE5ih6J7u2erhnOFjILClifksKcY8eIqfr3nMFQIpXlxq4ZEGn3O9ra5zZejYjg4vr1uapRkYV9\nYWFw//3w7bcQ5JwO/9P+nxj8zWDeGfwOz/d7Hh9V9tPW2M+Paa1aMSEsrOIK5gMPIP36kzj0dm4b\nbaNzZ23numKFDgd9222VH0q7f+v+rL9/PR9v+ZiHf3mYApt73O55C8vi49mXmcljLVp4uikAVPPx\nYWaHDjx+6BBp+WVzM9i+vX7ZioiAm2/WawTbt4f5D/+D7cmnYMkSHQqxKjJ1KoSElNm7jhdSVIZG\ncaYMLS6NM3lLq8/tMttQdUnJz2fAtm0ErlvHQ2Fh/JKQQM/Nm51+oTcYqiJlC7NXSUybNu3k9379\n+tGvX78y5T+YmcmH0dFsu/DC0w9kZGjXWy+8AH36OFXW+xve57V1r/HzbT/Tu1nFBmDGhYTw6bFj\nzDtxgtudVN6Lkpen3d2+v+kd3t09gIcavsasI0/TsGGFmuYSWjVsxdp713LTtzdx/cLrmT9qPnX9\nXOU/zXvILijgkYMHmdWhAzUqyWWdM/Rt0IABjRrxYng4M9q2LXP+WrX04sIxY2Dzinja3Hgzt6nP\naPxBRx55BNq1c32b3Y5S8MUXOiDRF1/oDrqQVatWsWrVKpeW6UIqbTFjRWW2oeqSWVDAtTt30qNu\nXX7p1u3kjO+m1FTu3LuXH+Pi+KRjR+qVMaqvweAOXCqzy2v7UXRD29cVZwM9G7jF7vc+IKiYtBW2\naRm+Y4dMDw8/88Cdd4qMGePUQqgCW4FM/nWydPqgkxxJOlLhNhXyT3KyhKxbJ+lltCdNShKZPl2k\neXO9nmvxYpH8o5HagHXtWpe1zxXk5ufKvYvvlV4f9ZLY9FhPN8fl/O/oUblh505PN8Mhx3NyJGDN\nGtmfkVH+Qmw2kWHDRB5/XCIjRZ56Sq/HGz5cZPXqqrOO8DR279ad2L7drdXgPhvoPsAKu99PUmQh\nYXFy1sm8KzndBvq0NMAK4OJi2uams2nwdnIKCmTw9u1y1549UuBAMGTm58stu3bJA/v2eaB13s2K\nhAT5MCpKvjp2TJbExUlaRZ0MGMpFRWS2K4fPFMWPeCwF7gJQSvUBkkUk1oV1n2RdSgrb0tN5uFmR\n2cZvvoFNm3QAiFKCkeQV5HHPknv4J+of1t67llYNW7msfX0aNOCyBg14LyrKqfQRETqqeJs2sGOH\nNt9euVKbd/qGNodPP9U2G4mJLmtjRanuW51Ph3/Kte2v5bLPLuNo8lFPN8llxOfm8nZkJK+3aePp\npjgkyM+Px1q04L9HjpS/kLff1qEMX36Z5s3hlVd0oM7Bg3VQzIsv1hZQbgqO6R46d4Y339SG31lZ\nnm5NedgEtFNKhSql/IDRaLlqT3Fy1pm8cLr8XgqMVkr5KaVaA+2AjS7tkaHKc9/+/dT08WFOx474\nOHiu1vL15eOOHVmRmMgfXvSM8iQiwivh4Yzbv59t6en8kpjIjMhIrtmxg5Qymt8ZPEx5NW/7DZgH\nxAA5QARwDzAOGGuX5gP0Su7tFHGXVKSscr9J2Gw2uWzrVvk8Jub0A4cO6dGnrVtLLSMjN0OunXet\nDP1mqGTkVmAUrwT2Z2RI4Nq1kpCbW2yaXbtE7rpLpFEj7U0jIqKEAidN0sODXjg0+N7696T5W81l\nZ6x3jtiWlclhYfIfBx5QvIn0/HwJXrdOtpTHb+HGjdqFy2HHbgnz80V+/FHkkktE2rUTmT1be/So\nEthsIrfeKvLQQ26rAve7sduPXtD3pLXPKTnrKK+1/3q0rXMWcAz4xe7YU1ZZxo2d4QxWJSVJ63/+\nkSwnZlOXx8dLq3/+OedHWfMKCmTsvn3Sc9MmicnOPrnfZrPJhAMH5KLNmyWxBL3A4HoqIrPdIugr\nslVEGC+Lj5fOGzZIvr0imZen3dW9+Wap+VOzU+XKz6+U27+/XXLz3fsnHrtvn0w5ePCM/evXi4wY\nIRIUJPLyyyKJiU4UlpMjcsEFIh9+6PqGuoBvdnwjTWY0kU3RleuT19VEZGWJ/5o1pwk+b2VmVJQM\n2ratbJnS07VWvGhRqUltNm3OMXSodk0+Y4br/Yy7heRkkVatRJYudUvx7lSgvXUzCvS5h81mkz5b\ntsjXx487nWfMnj0y8cABN7bK+7l1924ZuG2bpDp4kbDZbDIpLEx6bdpklOhKpCIy23tWQFUQmwhP\nHT7MK23a4Gs/lfTSS1C/fqm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ccIGTZh2BgXox4dSpldLGs4HEvDx2ZWQ4NaI5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"text/plain": [ "" ] }, "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=(-0.002,0.002))\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_array[i]\n", " if psi[1] < 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", " fac = np.pi*(m+1)/width\n", " exact = np.sin(fac*x)\n", " normalisation_factor = integrate_functions(exact,exact,dx)\n", " exact = exact/np.sqrt(normalisation_factor)\n", " psi = psi - exact\n", " ax2.plot(x,psi)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## A change of basis\n", "\n", "We have seen in lectures that to go from a matrix calculated in the basis $\\left\\{\\vert\\phi_n\\rangle\\right\\}$ to the basis $\\left\\{\\vert\\chi_a\\rangle\\right\\}$ we write $H^{(\\chi)}_{ab} = \\sum_{mn} S_{am}H^{(\\phi)}_{mn}\\left(S^\\dagger\\right)_{nb}$ with $S_{am} = \\langle \\chi_a\\vert\\phi_m\\rangle$ and $\\left(S^\\dagger\\right)_{nb} = \\langle \\phi_n\\vert \\chi_b\\rangle$. We can calculate this for the square well, treating the $\\phi$ basis set as our polynomial basis set and the $\\chi$ basis set as the eigenbasis. In this case, the Hamiltonian $H^{(\\chi)}$ should be diagonal, with the square well eigenvalues on the diagonal (because we have transformed representation into the eigenbasis)." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 0.999 0.000 -0.038 0.000 0.001 0.000 -0.000 0.000 0.000 -0.000\n", " 0.000 -0.991 -0.000 0.130 -0.000 -0.008 -0.000 0.000 -0.000 -0.000\n", " 0.037 -0.000 0.969 0.000 -0.245 -0.000 0.028 0.000 -0.002 0.000\n", " 0.000 -0.124 0.000 -0.921 -0.000 0.364 -0.000 -0.064 0.000 0.007\n", " 0.008 -0.000 0.226 -0.000 0.841 0.000 -0.477 0.000 0.117 -0.000\n", " 0.000 -0.037 0.000 -0.324 0.000 -0.728 -0.000 0.573 0.000 -0.185\n", " 0.003 -0.000 0.084 0.000 0.405 0.000 0.586 0.000 -0.642 -0.000\n", " -0.000 -0.015 0.000 -0.144 0.000 -0.457 -0.000 -0.422 -0.000 0.678\n", " 0.001 0.000 0.040 0.000 0.210 -0.000 0.475 0.000 0.248 0.000\n", " -0.000 -0.008 0.000 -0.076 -0.000 -0.272 -0.000 -0.457 -0.000 -0.075\n" ] } ], "source": [ "# Define the eigenbasis - normalisation needed elsewhere\n", "def Square_well_eigenbasis(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", "# These arrays will each hold an array of functions\n", "alternate_basis_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_array will start from 0\n", "for i in range(num_basis):\n", " n = i+1\n", " # Calculate A = \n", " integral = integrate_functions(Square_well_eigenbasis(n,width,1.0,x),Square_well_eigenbasis(n,width,1.0,x),dx)\n", " # Use 1/sqrt{A} as normalisation constant\n", " normalisation = 1.0/np.sqrt(integral)\n", " alternate_basis_array[i,:] = Square_well_eigenbasis(n,width,normalisation,x)\n", "\n", "# Now create the similarity matrix, S\n", "similarity_matrix = np.eye(num_basis)\n", "# Loop over basis functions chi_a (the bra in the matrix element)\n", "# Calculate and store the matrix elements \n", "for a 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", " similarity_matrix[a,m] = integrate_functions(alternate_basis_array[a],basis_array[m],dx)\n", " # The comma at the end prints without a new line; the %8.3f formats the number\n", " print \"%8.3f\" % similarity_matrix[a,m],\n", " # This print puts in a new line when we have finished looping over m\n", " print" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now that we have the matrix, we can transform from the polynomial basis to the eigenbasis." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Calculating S.H then S.H.S^{T}: \n", " 4.934 -0.000 -0.000 0.000 0.000 -0.000 -0.000 0.000 0.000 0.000\n", " -0.000 19.733 -0.000 -0.000 0.000 0.000 -0.000 -0.000 -0.000 0.000\n", " -0.000 0.000 44.380 -0.000 -0.001 -0.000 0.015 -0.000 -0.016 -0.000\n", " 0.000 -0.000 0.000 78.853 -0.000 -0.017 0.000 0.122 -0.000 -0.069\n", " 0.000 -0.000 -0.001 0.000 123.344 0.000 -2.580 0.000 2.241 -0.000\n", " 0.000 0.000 0.000 -0.017 -0.000 178.206 0.000 -7.399 -0.000 2.309\n", " -0.000 0.000 0.015 -0.000 -2.580 0.000 267.082 -0.000 -2.525 -0.000\n", " -0.000 -0.000 -0.000 0.122 0.000 -7.399 -0.000 357.306 -0.000 28.317\n", " 0.000 -0.000 -0.016 -0.000 2.241 -0.000 -2.525 0.000 233.413 -0.000\n", " 0.000 0.000 -0.000 -0.069 -0.000 2.309 -0.000 28.317 -0.000 218.559\n", "Calculating H.S^{T} then S.H.S^{T}: \n", " 4.934 -0.000 -0.000 0.000 0.000 -0.000 -0.000 0.000 0.000 0.000\n", " -0.000 19.733 -0.000 -0.000 0.000 0.000 -0.000 -0.000 -0.000 0.000\n", " -0.000 0.000 44.380 -0.000 -0.001 -0.000 0.015 -0.000 -0.016 -0.000\n", " 0.000 -0.000 0.000 78.853 -0.000 -0.017 0.000 0.122 -0.000 -0.069\n", " 0.000 -0.000 -0.001 0.000 123.344 0.000 -2.580 0.000 2.241 -0.000\n", " 0.000 0.000 0.000 -0.017 -0.000 178.206 0.000 -7.399 -0.000 2.309\n", " -0.000 0.000 0.015 -0.000 -2.580 0.000 267.082 -0.000 -2.525 -0.000\n", " -0.000 -0.000 -0.000 0.122 0.000 -7.399 -0.000 357.306 -0.000 28.317\n", " 0.000 -0.000 -0.016 -0.000 2.241 -0.000 -2.525 0.000 233.413 -0.000\n", " 0.000 0.000 -0.000 -0.069 -0.000 2.309 -0.000 28.317 -0.000 218.559\n" ] } ], "source": [ "print \"Calculating S.H then S.H.S^{T}: \"\n", "similarity_matrix_x_H = np.dot(similarity_matrix,H_Matrix)\n", "alt_H = np.dot(similarity_matrix_x_H,similarity_matrix.T)\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", " # The comma at the end prints without a new line; the %8.3f formats the number\n", " print \"%8.3f\" % alt_H[n,m],\n", " # This print puts in a new line when we have finished looping over m\n", " print\n", " \n", "# There is no need to do this - it should give exactly the same result\n", "# But it is a useful consistency check and may give a hint to any asymmetries\n", "print \"Calculating H.S^{T} then S.H.S^{T}: \"\n", "similarity_matrix_x_H = np.dot(H_Matrix,similarity_matrix.T)\n", "alt_H2 = np.dot(similarity_matrix,similarity_matrix_x_H)\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", " # The comma at the end prints without a new line; the %8.3f formats the number\n", " print \"%8.3f\" % alt_H2[n,m],\n", " # This print puts in a new line when we have finished looping over m\n", " print" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " Poly Eigen Difference\n", " 4.934 4.935 -0.000\n", " 19.733 19.739 -0.006\n", " 44.380 44.413 -0.033\n", " 78.853 78.957 -0.104\n", " 123.344 123.370 -0.026\n", " 178.206 177.653 0.553\n", " 267.082 241.805 25.277\n", " 357.306 315.827 41.478\n", " 233.413 399.719 -166.306\n", " 218.559 493.480 -274.921\n" ] } ], "source": [ "# Print the diagonal of the Hamiltonian from polynomial basis (Poly), the exact eigenvalue (Eigen) and the difference\n", "print \" Poly Eigen Difference\"\n", "for i in range(num_basis):\n", " n = i+1\n", " print \"%8.3f %8.3f %8.3f\" %(alt_H[i,i], n*n*np.pi*np.pi/2.0,alt_H[i,i]-n*n*np.pi*np.pi/2.0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that, for the first few (I would say five) eigenvalues this is very accurate. After that, errors start to creep in, just as we saw for the eigenvalues we calculated by diagonalising the Hamiltonian in the polynomial basis. This is again a manifestation of the truncated, approximate basis failing to represent the high energy states of the well accurately." ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.11" } }, "nbformat": 4, "nbformat_minor": 0 }