{ "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": [], "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 two functions over the width of the well\n", "def integrate_functions(f1,f2,size_x,dx):\n", " \"\"\"Integrate two functions over defined x range\"\"\"\n", " sum = 0.0\n", " for i in range(size_x):\n", " sum = sum + f1[i]*f2[i]\n", " sum = sum*dx\n", " return sum\n", "\n", "\n" ] }, { "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 `d2_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", "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 -0.000 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D3/5GbdVX7UqzzWYjJyeHjIwMmps7Mmd4szQDjDSbOSU0lP+Wdo9nMI8xY91i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\nlj7ypPGkry/ccw+sXUvND3/A13lf897895peVFAA+/a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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", "d2basis_array = np.zeros((num_basis,num_x_points))\n", "\n", "def poly(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 d2_finite(f,dx):\n", " d2 = np.zeros(f.size)\n", " for i in range(1,f.size-1):\n", " d2[i] = (f[i+1] + f[i-1] - 2.0*f[i])/(dx*dx)\n", " d2[0] = (f[1]-2.0*f[0])/(dx*dx)\n", " d2[f.size-1] = (f[f.size-2]-2.0*f[f.size-1])/(dx*dx)\n", " return d2\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,:] = poly(x,i,width)\n", " norm = integrate_functions(basis_array[i,:],basis_array[i,:],num_x_points,dx)\n", " basis_array[i,:] = basis_array[i,:]/np.sqrt(norm)\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,:],num_x_points,dx)\n", " basis_array[i,:] = basis_array[i,:] - overlap*basis_array[j,:]\n", " norm = integrate_functions(basis_array[i,:],basis_array[i,:],num_x_points,dx)\n", " basis_array[i,:] = basis_array[i,:]/np.sqrt(norm)\n", " d2basis_array[i,:] = d2_finite(basis_array[i,:],dx)\n", " ax2.plot(x,basis_array[i,:])\n", " \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,:],num_x_points,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", "Hmat = np.eye(num_basis)\n", "\n", "# Define a function to act on a basis function with the potential\n", "def add_pot_on_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*d2basis_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,num_x_points,dx)\n", " Hmat[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 -8.1102e-15 -3.7010e-02 5.7791e-16 8.0193e-03\n", " 7.5277e-17 3.1466e-03 1.8386e-18 -1.0064e-03 1.1512e-17]\n", "[ -8.0699e-15 -9.9144e-01 -2.1094e-15 -1.2393e-01 1.2212e-15\n", " 3.7062e-02 2.7756e-16 -1.6914e-02 -1.6653e-16 5.3650e-03]\n", "[ -3.8006e-02 2.3315e-15 -9.6852e-01 2.6645e-15 2.2668e-01\n", " 1.9082e-16 9.0925e-02 -1.4225e-16 -2.9471e-02 -5.2042e-18]\n" ] } ], "source": [ "# Solve using linalg module of numpy (which we've imported as la above)\n", "eigval, eigvec = la.eigh(Hmat)\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 eigval\n", "print eigvec[0]\n", "print eigvec[1]\n", "print eigvec[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\" % (eigval[i],n*n*np.pi*np.pi/2.0,eigval[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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6pUlVsWGDvlceeADuu88nhjKM0WwwGAzVB2M0l8HqtDTG7NzJ77160bNRo1ML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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+eigvec[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", " norm = integrate_functions(exact,exact,num_x_points,dx)\n", " exact = exact/np.sqrt(norm)\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 eigenbasis_sw(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", "alt_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(eigenbasis_sw(n,width,1.0,x),eigenbasis_sw(n,width,1.0,x),num_x_points,dx)\n", " # Use 1/sqrt{A} as normalisation constant\n", " normalisation = 1.0/np.sqrt(integral)\n", " alt_basis_array[i,:] = eigenbasis_sw(n,width,normalisation,x)\n", "\n", "# Now create the similarity matrix, S\n", "Smat = 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", " Smat[a,m] = integrate_functions(alt_basis_array[a],basis_array[m],num_x_points,dx)\n", " # The comma at the end prints without a new line; the %8.3f formats the number\n", " print \"%8.3f\" % Smat[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": 8, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Calculating S.H then S.H.ST: \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.ST then S.H.ST: \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.ST: \"\n", "SH = np.dot(Smat,Hmat)\n", "alt_H = np.dot(SH,Smat.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.ST then S.H.ST: \"\n", "HS = np.dot(Hmat,Smat.T)\n", "alt_H2 = np.dot(Smat,HS)\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." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "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": "2.7.10" } }, "nbformat": 4, "nbformat_minor": 0 }