{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "\\pagestyle{plain} %For page numbering in PDF version."
     ]
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Electron Orbital Visualization"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This notebook was developed for the Quantum Chemistry graduate course (CHM 6470 - Chemical Bonding and Spectra I) at the University of Florida.  It used the Hydrogen atom wavefunctions to provide visualizations of the quantum equations of the atomic orbitals. The visualization requires the use of the \"mayavi2\" library to display isoplots (surfaces of equal value) of the probability density functions. It is these functions that can be interpreted as describing the most probable location for finding an electron."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Usage:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "*To use this notebook start it with the following command:*\n",
      "\n",
      "    ipython notebook\n",
      "    \n",
      "Authors:\n",
      "\n",
      "* Damon Allen Ph.D. \n",
      "* [Nick Polfer Ph.D.](http://www.chem.ufl.edu/~polfer/)\n",
      "* Corey Stedwell Ph.D. Candidate \n",
      "\n",
      "Debugging help from:\n",
      "\n",
      "* Nathan Roehr Ph.D. Candidate "
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Acknowledgements"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This project is financially supported by the National Science Foundation under grant CHE-0845450.\n",
      "\n",
      "*The information in this notebook is partially based on the information found at the following sites:*\n",
      "\n",
      "[http://panda.unm.edu/Courses/Finley/P262/Hydrogen/WaveFcns.html](http://panda.unm.edu/Courses/Finley/P262/Hydrogen/WaveFcns.html)\n",
      "\n",
      "[http://www.hasenkopf2000.net/wiki/page/3d-hydrogen-structure-python/](http://www.hasenkopf2000.net/wiki/page/3d-hydrogen-structure-python/)\n",
      "\n",
      "[http://www.sethanil.com/python-for-reseach/5](http://www.sethanil.com/python-for-reseach/5)"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Sample output using quantum number values of $n=3$, $l=2$, $m=0$ "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<a href=\"https://github.com/damontallen/Orbitals/raw/master/n_3-l_2-m_0_opaque\"><img src=\"https://github.com/damontallen/Orbitals/raw/master/n_3-l_2-m_0_opaque.png\" title=\"Orbital with 50% opacity\" width=50% height=50% /></a>\n",
      "\n",
      "\n",
      "* Number of contours used  = 16\n",
      "* Opacity = 0.5"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Quantum Equations"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The [(radial) probability function](http://www.chemistry.mcmaster.ca/esam/Chapter_3/section_2.html) can be expressed as the product of the square of the [wavefunction](http://en.wikipedia.org/wiki/Hydrogen_atom#Wavefunction) ($\\psi$) times the square of the distance (r) from the nucleus."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "$P = \\psi^2 r^2$ (probability function)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$\\psi$ is a wavefunction that is composed of the radial ($R_{nl}$) and the spherical harmonics ($Y_{lm}$) functions. $R_{nl}$ is dependent on the distance from the center of the atom $r$, and the principal quantum number $n$, and angular momentum quantum number $l$.  $Y_{lm}$ is a function of $l$, the magnetic angular momentum $m_l$, $\\phi$ (defined as the angle of the positon vector in the $\\textbf{xy}$ plane), and $\\theta$ (i.e., angle between $\\textbf{z}$-axis and position vector) in a spherical coordinate system.  For the purposes of this notebook $m_l$ will be expressed simply by the term $m$ to avoid confusion with $l$.\n",
      "\n",
      "<img src=\"http://lowrank.net/gnuplot/spherical_harmonics/coordinate2.png\" alt=\"coords\" />\n",
      "\n",
      "$$\\psi_{nlm}(r,\\theta,\\phi) = R_{nl}(r)Y_{lm}(\\theta,\\phi)$$\n",
      "\n",
      "*(Note: In the following derivations for $\\psi$, $R$ and $Y$'s the quantum number subscripts are dropped in order to prevent confusion with multiplication terms.)*"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Where:\n",
      "\n",
      "$$R(r) = \\left(\\frac{2\\cdot z}{n\\cdot a_0}\\right)^{3/2} \\sqrt{\\frac{(n-l-1)!}{2\\cdot n\\cdot [(n+l)!]^3}}\\cdot exp\\left(\\frac{-z\\cdot r}{n \\cdot a_0}\\right) \\cdot \\left(\\frac{2\\cdot z\\cdot r}{n \\cdot a_0} \\right)^l \\cdot L^{2\\cdot l +1}_{n-l-1}  \\left(\\frac{2 \\cdot z \\cdot r}{n\\cdot a_0} \\right)$$\n",
      "\n",
      "Where:\n",
      "\n",
      "$z$ refers to the atomic charge of the nucleus (i.e., +1 for hydrogen)\n",
      "\n",
      "$a_0$ refers to the Bohr radius (assume $a_0 = 1$ for unity)\n",
      "\n",
      "and $L$ is a [Laguerre polynomial](http://en.wikipedia.org/wiki/Laguerre_polynomials):\n",
      "\n",
      "$$\\hspace{20 mm}\\text{Where: } L^{2\\cdot l +1}_{n-l-1}\\left(\\frac{2 \\cdot z \\cdot r}{n\\cdot a_0} \\right) = \\sum_{i=0}^{n-l-1}{\\frac{(-i)^i\\cdot\\left((n+l)!\\right)^2 \\left( \\frac {2zr}{n a_0}\\right)^i} {i!\\cdot(n-l-1-i)!\\cdot(2\\cdot l+1+i)!}}$$\n",
      "\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$$\\text{ }$$\n",
      "\n",
      "$$Y^{m}_{l}(\\theta,\\phi)=(-1)^{|m|}\\cdot\\sqrt{\\frac{(2\\cdot l+1)(l-|m|)!}{4\\cdot\\pi\\cdot (l+|m|)!}}\\cdot e^{i\\cdot m \\cdot\\phi}\\cdot P^{|m|}_{l}(cos(\\theta))$$\n",
      "\n",
      "Where $P_l^m$ is a [Legendre polynomial](http://en.wikipedia.org/wiki/Legendre_polynomials).\n",
      "\n",
      "$$\\hspace{20 mm}\\text{Where: }P^{|m|}_{l}(cos(\\theta))=\\left(1-cos^2(\\theta)\\right)^{\\left|\\frac{m}{2}\\right|} \\cdot \\frac{\\delta^{|m|} }{\\delta (cos(\\theta))^{|m|}}(P_l(cos(\\theta)))$$\n",
      "\n",
      "$$\\hspace{20 mm}\\text{Where: }P^{|m|}_{l}(cos(\\theta))=sin^{\\left|m\\right|}(\\theta) \\cdot \\frac{\\delta^{|m|} }{\\delta (cos(\\theta))^{|m|}}(P_l(cos(\\theta)))$$\n",
      "\n",
      "$\\hspace{20 mm}$[Rodrigues\u2019 formula](http://en.wikipedia.org/wiki/Rodrigues%27_formula) provides a solution to the Legendre polynomial $P_l$.\n",
      "\n",
      "$$\\hspace{20 mm}\\hspace{20 mm}\\text{and where: }P_l(cos(\\theta)) = \\frac{1}{2^l\\cdot l!} \\frac{d^l}{d (cos(\\theta))^l} (cos^2(\\theta)-1)^l$$\n",
      "\n",
      "*(Note that the $\\delta^m$ term refers refers to the derivative with order m with respect to $cos(\\theta)$ and the $d^l$ term refers to the derivative with order $l$ with respect to $cos(\\theta)$.)*"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Displaying the Orbitals"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For purposes of display we are only intrested in the real portion of $Y^{m}_{l}(\\theta,\\phi)$.\n",
      "\n",
      "Specifically, if $m\\ne0$ then we evaluate $Y$ in with the following modifications.\n",
      "\n",
      "For the real part:\n",
      "\n",
      "$$Y^{m}_{l}(\\theta,\\phi)=\\left|\\sqrt{\\frac{(2\\cdot l+1)(l-|m|)!}{4\\cdot\\pi\\cdot (l+|m|)!}}\\cdot \\left(\\sqrt{2} \\cdot \\Re\\left\\{e^{i\\cdot m \\cdot\\phi}\\right\\}\\right)\\cdot P^{|m|}_{l}(cos(\\theta))\\right|$$  (If $m>0$)\n",
      "\n",
      "*(Note that the $(-1)^{|m|}$ goes away when only using the real or imaginary portions but you have to take the absolute value.)*\n",
      "\n",
      "*(Note that $\\Re\\left\\{e^{i\\cdot m \\cdot\\phi}\\right\\}$ denotes the real part of $e^{i\\cdot m \\cdot\\phi}$)*\n",
      "\n",
      "or, for the imaginary part:\n",
      "\n",
      "$$Y^{m}_{l}(\\theta,\\phi)=\\left|\\sqrt{\\frac{(2\\cdot l+1)(l-|m|)!}{4\\cdot\\pi\\cdot (l+|m|)!}}\\cdot \\left(\\sqrt{2} \\cdot \\Im\\left\\{e^{i\\cdot m \\cdot\\phi}\\right\\}\\right)\\cdot P^{|m|}_{l}(cos(\\theta))\\right|$$  (If $m<0$)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "*(Note that the real and imaginary portions are multiplied with a scaling factor equal to $\\frac{2}{\\sqrt{2}} = \\sqrt{2}$)*"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Notes on computational alternatives:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "When solving the real or imaginary portions by hand the [Euler's formula](http://en.wikipedia.org/wiki/Euler%27s_formula) is used and the results are added up.\n",
      "\n",
      "For example, if $l=1$ and $m=1$,  the real solution is:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$=\\frac{1}{2}\\cdot\\sqrt{\\frac{3}{2\\cdot\\pi}}\\cdot sin(\\theta)\\cdot\\left(cos(\\phi)-i\\cdot sin(\\phi) + cos(\\phi)+i\\cdot sin(\\phi) \\right)$\n",
      "\n",
      "$=\\frac{1}{2}\\cdot\\sqrt{\\frac{3}{2\\cdot\\pi}}\\cdot sin(\\theta)\\cdot\\left(cos(\\phi) + cos(\\phi) \\right)$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$=\\frac{1}{2}\\cdot\\sqrt{\\frac{3}{2\\cdot\\pi}}\\cdot sin(\\theta)\\cdot 2 \\cdot cos(\\phi) $"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$=\\sqrt{\\frac{3}{2\\cdot\\pi}}\\cdot sin(\\theta)\\cdot  cos(\\phi) $"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This result needs to be scaled scaling by a factor $\\frac{1}{\\sqrt{2}}$.\n",
      "\n",
      "$=\\frac{1}{\\sqrt{2}}\\cdot\\sqrt{\\frac{3}{2\\cdot\\pi}}\\cdot sin(\\theta)\\cdot  cos(\\phi) $\n",
      "\n",
      "$=\\sqrt{\\frac{3}{4\\cdot\\pi}}\\cdot sin(\\theta)\\cdot  cos(\\phi) $"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Import Libraries:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In order to have mayavi.mlab display correctly, version 2.7 of Python must be used."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import sys #texting for the right version of Python to use with mayavi\n",
      "print(\"Python version = {}\".format(sys.version))\n",
      "print(\"Machine readable Python version = {}\".format(sys.version_info))\n",
      "sys.version_info[0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Python version = 2.7.5+ (default, Sep 19 2013, 13:48:49) \n",
        "[GCC 4.8.1]\n",
        "Machine readable Python version = sys.version_info(major=2, minor=7, micro=5, releaselevel='final', serial=0)\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 1,
       "text": [
        "2"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Additionally, this notebook uses the *sympy* library to symbolically develop the equations needed to calculate the probability function to the wave equation.  Once derived these equations are converted to *numpy* versions for speed and compatibility with the *mayavi* library.\n",
      "\n",
      "*(Note: To install mayavi2 on Ubuntu 12.04, type \"sudo apt-get install mayavi2\" in the terminal window.)*"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(\"The library version numbers used in this notebook are:\")\n",
      "if sys.version_info[0]==2:\n",
      "    #this requires the use of no higher than python 2.7 \n",
      "    from mayavi import __version__ as mayavi_version  \n",
      "#     import scipy.special\n",
      "#     import scipy.misc\n",
      "    from mayavi import mlab\n",
      "    print(\"mayavi version:  %s\"%mayavi_version)\n",
      "else:\n",
      "    print(\"The use of mayavi.mlab to display the orbital requires the \"+\\\n",
      "          \"use of Python 2.7.3\")\n",
      " \n",
      "from IPython import __version__ as IPython_version \n",
      "from IPython.display import Latex\n",
      "import numpy as np\n",
      "import sympy\n",
      "\n",
      "#\"I\" is sympy's imaginary number\n",
      "from sympy import symbols,I,latex,pi,diff \n",
      "from sympy.utilities.lambdify import lambdastr\n",
      "from sympy import factorial as fac\n",
      "from sympy.functions import Abs,sqrt,exp,cos,sin\n",
      "from sympy import re, im, simplify\n",
      "\n",
      "#display the latex representation of a symbolic variable by default.\n",
      "from sympy import init_printing \n",
      "init_printing(use_unicode=True)\n",
      "\n",
      "a_0,z,r=symbols(\"a_0,z,r\")\n",
      "n,m,l=symbols(\"n,m,l\",integer=True)\n",
      "int_m=symbols(\"int_m\",integer=True)\n",
      "theta,phi = symbols(\"\\\\theta,\\\\phi\",real=True)\n",
      "\n",
      "#The variables will used with lambdify...\n",
      "angle_theta, angle_phi, radius = symbols(\"angle_theta,angle_phi,radius\",\n",
      "                                         real=True)\n",
      "\n",
      "\n",
      "print(\"numpy version:   %s\"%np.__version__)\n",
      "print(\"sympy version:   %s\"%sympy.__version__)\n",
      "\n",
      "print(\"IPython version: %s\"%IPython_version)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The library version numbers used in this notebook are:\n",
        "mayavi version:  4.1.0"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "numpy version:   1.7.1"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "sympy version:   0.7.4.1\n",
        "IPython version: 1.2.0\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "*(Note: Even though the SciPy library has both the Laguerre and and spherical harmonics functions in it, for purposes of clarity in the derivation and consistency in the way orbitals have been traditionally represented in Chemistry, specific solutions of these functions are developed and written here.)*"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Declare Functions:"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Defining $P_l$ (Legendre polynomial):"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$$P_l(cos(\\theta)) = \\frac{1}{2^l\\cdot l!} \\frac{d^l}{d (cos(\\theta))^l} (cos^2(\\theta)-1)^l$$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def P_l(l,theta): #valid for l greater than equal to zero\n",
      "    \"\"\"Legendre polynomial\"\"\"\n",
      "    if l>=0:\n",
      "        eq=diff((cos(theta)**2-1)**l,cos(theta),l)\n",
      "    else:\n",
      "        print(\"l must be an integer equal to 0 or greater\")\n",
      "        raise ValueError\n",
      "    return 1/(2**l*fac(l))*eq"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Validation"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "P_l(0,theta)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$1$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAAgAAAAPBAMAAAArJJMAAAAAJFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAADHJj5lAAAAC3RSTlMAzRAiu5mrdu/dZmiL4QAAAAAJcEhZcwAA\nDsQAAA7EAZUrDhsAAAAjSURBVAgdY2BgEGJgYDDZxMCgEgYkGNhJJVgzdmYB9TEwAACPpQrvlUCH\ncAAAAABJRU5ErkJggg==\n",
       "prompt_number": 4,
       "text": [
        "1"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "P_l(1,theta)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\cos{\\left (\\theta \\right )}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAADcAAAAVBAMAAAAQkWtIAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEJmJVCLvMs1Edmar\n3bti/yyrAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABR0lEQVQoFZWRPUgDQRCFv0ty5oL5I4KVYFBE\nsAqohVHxahuvsrGQiFYWpgqoSA5s7NzCPmIa0eYQxNLUkiIg1qZOFTVNEMHZHCdJSOMrdt7OezM7\nuwv/w6lvfxpVZTYlezdPvDhCtdKQtCfBHSFWJTdDSqHJMA4g+kHKQ4qHEWtI1xplD8uGzOISRr6q\nONm8FWc4C7uKZ6WZuU/JOXNoGU0SIiY92KjXj9KMu1guW8VXKB8XCIuYsOECfiDSYFraRDuQyr23\nHBHHFHwR/ZZsm8q1eLoiNicuP33R6BBq98S/yjlHT6HbGl3pAzK3nIm9B5WrHHHPH6jLuvSQgcxD\nwk6pyHmkQNKRq9TgxZSXIJSFqYVlzNk1FVu9X5GUfoTMjbiwlCxDeAv22wHpiw8BzwekL+qDNQy3\nFwaX3mdLKjANqjv+9hF+AYl+SPalOE9dAAAAAElFTkSuQmCC\n",
       "prompt_number": 5,
       "text": [
        "cos(\\theta)"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "P_l(2,theta)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\frac{1}{2} \\left(3 \\cos^{2}{\\left (\\theta \\right )} - 1\\right)$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAJUAAAAqBAMAAABIEATcAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\ngg==\n",
       "prompt_number": 6,
       "text": [
        "     2            \n",
        "3\u22c5cos (\\theta) - 1\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "        2         "
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Defining $P^{|m|}_{l}$ (Legendre polynomial):"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$$P^{|m|}_{l}(cos(\\theta))=\\left(1-cos^2(\\theta)\\right)^{\\left|\\frac{m}{2}\\right|} \\cdot  {\\frac{\\delta^{|m|} }{\\delta (cos(\\theta))^{|m|}}(P_l(cos(\\theta)))}$$\n",
      "\n",
      "Which equals...\n",
      "\n",
      "$$P^{|m|}_{l}(cos(\\theta))=sin^{\\left|m\\right|}(\\theta) \\cdot  {\\frac{\\delta^{|m|} }{\\delta (cos(\\theta))^{|m|}}(P_l(cos(\\theta)))}$$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def P_l_m(m,l,theta):\n",
      "    \"\"\"Legendre polynomial\"\"\"\n",
      "    eq = diff(P_l(l,theta),cos(theta),Abs(m))\n",
      "    result = sin(theta)**Abs(m)*eq #note 1-cos^2(theta) = sin^2(theta)\n",
      "    return result"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Validation"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "P_l_m(1,1,theta) #Because sqrt(1-cos^(theta)) = sin(theta)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\sin{\\left (\\theta \\right )}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAADUAAAAVBAMAAAAUZLt1AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAMnZUzRC73UTviSKZ\nZqszMyTAAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABO0lEQVQoFZWRMUjDUBCGv2DTatMaFVdrqZuK\nZBJ0yiDOmQTBwUEEEaS7S1YdXRUsIjjqJEgR6+4QHVWwCo6Woqi1ovVe0pjGzRve/e++u597Cfwn\nhoLmy/aMthUNG4uiC+f09gU1rRmxhANJax7sqBaqUREXmC5K/Ilt0F4xPWRUhdEfZDm7i2JZZdgj\nYaGNFOzjbwZ3BibywtIVOHO5c5WagyJrMJs3PoUlPTis1XYdsjYbDiXFVuBLWMqCGXiHriKptzEU\nW4JnYT0uNNGkTauj77cqii3/Mv2FTN1nZbKNDiaeegOz5G88DU8dTO3S4EDcZZcph1Vl2PZMV+HB\nkA9ApsLm1bWbaz3mWveTH1JXb18YPxKWcOWIx3p4PQlFlG9DuReKKCeVn4Ru+yl2+P9WKmFPDJ4G\ntxv4AQBlUOV8BEbWAAAAAElFTkSuQmCC\n",
       "prompt_number": 8,
       "text": [
        "sin(\\theta)"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "P_l_m(-1,1,theta) "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\sin{\\left (\\theta \\right )}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAADUAAAAVBAMAAAAUZLt1AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAMnZUzRC73UTviSKZ\nZqszMyTAAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABO0lEQVQoFZWRMUjDUBCGv2DTatMaFVdrqZuK\nZBJ0yiDOmQTBwUEEEaS7S1YdXRUsIjjqJEgR6+4QHVWwCo6Woqi1ovVe0pjGzRve/e++u597Cfwn\nhoLmy/aMthUNG4uiC+f09gU1rRmxhANJax7sqBaqUREXmC5K/Ilt0F4xPWRUhdEfZDm7i2JZZdgj\nYaGNFOzjbwZ3BibywtIVOHO5c5WagyJrMJs3PoUlPTis1XYdsjYbDiXFVuBLWMqCGXiHriKptzEU\nW4JnYT0uNNGkTauj77cqii3/Mv2FTN1nZbKNDiaeegOz5G88DU8dTO3S4EDcZZcph1Vl2PZMV+HB\nkA9ApsLm1bWbaz3mWveTH1JXb18YPxKWcOWIx3p4PQlFlG9DuReKKCeVn4Ru+yl2+P9WKmFPDJ4G\ntxv4AQBlUOV8BEbWAAAAAElFTkSuQmCC\n",
       "prompt_number": 9,
       "text": [
        "sin(\\theta)"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Defining $Y^{m}_{l}(\\theta,\\phi)$ (Spherical harmonics):"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$$Y^{m}_{l}(\\theta,\\phi)=\\left|\\sqrt{\\frac{(2\\cdot l+1)(l-|m|)!}{4\\cdot\\pi\\cdot (l+|m|)!}}\\cdot \\left(\\sqrt{2} \\cdot \\Re\\left\\{e^{i\\cdot m \\cdot\\phi}\\right\\}\\right)\\cdot P^{|m|}_{l}(cos(\\theta))\\right|$$  (If $m>0$)\n",
      "\n",
      "or\n",
      "\n",
      "$$Y^{m}_{l}(\\theta,\\phi)=\\left|\\sqrt{\\frac{(2\\cdot l+1)(l-|m|)!}{4\\cdot\\pi\\cdot (l+|m|)!}}\\cdot \\left(\\sqrt{2} \\cdot \\Im\\left\\{e^{i\\cdot m \\cdot\\phi}\\right\\}\\right)\\cdot P^{|m|}_{l}(cos(\\theta))\\right|$$  (If $m<0$)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def Y_l_m(l,m,phi,theta):\n",
      "    \"\"\"Spherical harmonics\"\"\"\n",
      "    eq = P_l_m(m,l,theta)\n",
      "    if m>0:\n",
      "        pe=re(exp(I*m*phi))*sqrt(2)\n",
      "    elif m<0:\n",
      "        pe=im(exp(I*m*phi))*sqrt(2)\n",
      "    elif m==0:\n",
      "        pe=1\n",
      "    return abs(sqrt(((2*l+1)*fac(l-Abs(m)))/(4*pi*fac(l+Abs(m))))*pe*eq)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Validation"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Y_l_m(0,0,phi,theta)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\frac{1}{2 \\sqrt{\\pi}}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAACkAAAAwBAMAAAB+l06WAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAzRAiu5mrdu/dZjKJ\nRFRer8KoAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABEklEQVQ4EWNggAMhOAuJYfIJiQNjqoRhE2Vg\nH76irBk/s2C+H3r0fyzgA328YQ+xGs2yXDjfNMQbxmYWgLGYEhjOX4ByWB/ARNkUGDgaoBxNmCAD\nxwQGtt9QXhxclPETXJRpAlwUyOCEplGeBQzsIKcFgCXvH4CoARp7Zl/xcmMIbwqEYqhi4H7AY1AN\n4bE6MDDwghwHMpaFIQkiWgakKgQYGNgLgIxtYDkGBr4ABmNm9b9AS0GKohggVm9lYChmYPrCwLAG\nKMj0iQEoz8DAPOdMGNDAeAOGSUAe+wSGHpAoI9CBQFH7AK4DQB7LAoYckCgUsH3iVICxETT3n6cI\nDoIlIYRgI1jvAxBsBIvRAMFmAAAH6VvpoGG8TAAAAABJRU5ErkJggg==\n",
       "prompt_number": 11,
       "text": [
        "   1   \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "    ___\n",
        "2\u22c5\u2572\u2571 \u03c0 "
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Y_l_m(1,0,phi,theta)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\frac{\\sqrt{3}}{2 \\sqrt{\\pi}} \\left\\lvert{\\cos{\\left (\\theta \\right )}}\\right\\rvert$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAHIAAAA0BAMAAACk8nE/AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nTkSuQmCC\n",
       "prompt_number": 12,
       "text": [
        "  ___              \n",
        "\u2572\u2571 3 \u22c5\u2502cos(\\theta)\u2502\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "          ___      \n",
        "      2\u22c5\u2572\u2571 \u03c0       "
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "l=1\n",
      "m=-1\n",
      "Y_l_m(l,m,phi,theta)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\frac{\\sqrt{3}}{2 \\sqrt{\\pi}} \\left\\lvert{\\sin{\\left (\\phi \\right )} \\sin{\\left (\\theta \\right )}}\\right\\rvert$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAKwAAAA0BAMAAADlKs7FAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nAAAASUVORK5CYII=\n",
       "prompt_number": 13,
       "text": [
        "  ___                        \n",
        "\u2572\u2571 3 \u22c5\u2502sin(\\phi)\u22c5sin(\\theta)\u2502\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "               ___           \n",
        "           2\u22c5\u2572\u2571 \u03c0            "
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "l=1\n",
      "m=1\n",
      "Y_l_m(l,m,phi,theta)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\frac{\\sqrt{3}}{2 \\sqrt{\\pi}} \\left\\lvert{\\sin{\\left (\\theta \\right )} \\cos{\\left (\\phi \\right )}}\\right\\rvert$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAK4AAAA0BAMAAADh3x74AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAInarRM2ZVBDdiWbv\nuzJCz3LGAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAEK0lEQVRYCa2WXWgcVRTH/7O7k539mmxe8mJC\nJikotMUGU0pRKPPgi1IwDxZ9UBgopqBU1xfBomQRFCoK2xcVQVx1FVyQrgV9qKipiA+itaUIgh8N\nDUZQaG1d6xpN1v+5MzczyYRIk3tg7z3n3HN/995zZ2YPEMtYXyS2TWl7TYHWcqzptbYpa6BmirSW\nc3ytacw6Aqv9nvk9Ow0MI/+PsW1qULGDPTX8rU1jPdN70Hf+NMbToF2imM1DzieyIVw7kNaU7OYb\nkfFI+/UlU0jhWM90gYIiFs+aBDvLwOkQ+FXdJPixKl4hbwi4aPTFGAtKTXL7dVzsmNxvtleok/c1\n8HrVJNddekJwHyF/TWMf18qWej37gftlem7mqK8xLa3E/W+h+knsSWpulMHSPL169myQDBE9HHE/\ni/3WOeoTjyI7H/sS2qjSPeAAFc21U2mNuEvxTLsOVGovANOxL6GpE6PJd5ZOzU2MR2p6ZCdHZjDo\nQ5SUZJrKxVa09Gw1yiY9cgZwexjsgFtOS1mdWL40ztxGs/WMkGtd1jZyDaZhElc6sGurzli5S6kZ\nae/bnOveMjE9+gd+/uLSDo/RxQAY8/GprzQ4D7dreH6iBQnj8Dv8YfGhKW6bavq0MizSwovy7bwA\nPOhZV+modICTU1Pf1FESzkjNPeOeQMVTYcD39GW/K1rM1gebcw/Webvk/gDIv16hBhyC/FHlGzQP\nIb9SaMJdUWHAy/RdwJ04DDwpXFU7rWt+Z0wLheVxCcW3gLyFZR9YgsslXI471+m6wqWWVBjwOR+E\nHjfyLt2b79d5ux8I98dVrvMXBsgUbk6WmuVSyypMcQsBuYz+H+4QSt0El3lwuhhsktlI7Pe6ClN5\nGPQcj0uDj8Zm93YMuCPBlXvryjHDe2Oq8+UAua4KU/dme/n5bLDRvY2FiQalhafqOC/HivJQnARu\nk+vGAOdipIM33LOwmyoMeEvOUcQ+Ds2k9puoVFu4+9Rpf6G/f6F/4Ol/yZTTP3dzlfNsn42zb2cV\nw+29Kow2D4/Fj4/Ns7tXcYeP/kRdSbJSTWfohA4b0UqyL8iKN4nHmhOuM4mTvpiUZKWa5n4YBgFv\naiXZlwJa74un6Ak3W0d5TkzK8bBTbZpbkR1RnOmwX9eep90U37P8tVBuILsiJuVI2Kk2zVXfdY5p\nfiJY1FH+PFFkgRbs3irXaYg7klu1Evcqe9FhY6/WrE6oleRYanahF3pYqWbkQQtCc9vtPc0QwfS2\nfxk/NbRtYAR4Lep3wa0VqxskYGsLDZzjQ+9zrqS3gv1bo6Rn7aBrtVJdCOvgdNQNe/IBhuJK9RFE\nl3jDnPUTFoFx6ErV6fGbZUSsV9uHmdioUs008KURLGw+sORGlSo/sreb4UaUqFI1yhRYVKka5yKs\nVM1zZwPzTCGmK9VtrfMf6yYrqeVxYhUAAAAASUVORK5CYII=\n",
       "prompt_number": 14,
       "text": [
        "  ___                        \n",
        "\u2572\u2571 3 \u22c5\u2502sin(\\theta)\u22c5cos(\\phi)\u2502\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "               ___           \n",
        "           2\u22c5\u2572\u2571 \u03c0            "
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(Y_l_m(1,1,phi,theta)) #showing the computer's version of symbolic"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "sqrt(3)*Abs(sin(\\theta)*cos(\\phi))/(2*sqrt(pi))\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Defining L, R, $\\psi$, and the probability function P:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$$R(r) = \\left(\\rho \\right)^{3/2} \\sqrt{\\frac{(n-l-1)!}{2\\cdot n\\cdot [(n+l)!]^3}}\\cdot e^{\\frac{-z}{n \\cdot a_0}\\cdot r} \\left(\\rho \\right)^l \\cdot L^{2\\cdot l +1}_{n-l-1}  \\left(\\rho \\right)$$\n",
      "\n",
      "$$\\text{Where: }$$\n",
      "\n",
      "$$\\hspace{20 mm} L^{2\\cdot l +1}_{n-l-1}\\left(\\rho \\right) = \\sum_{i=0}^{n-l-1}{\\frac{(-i)^i\\cdot\\left((n+l)!\\right)^2 \\left( \\rho \\right)^i} {i!\\cdot(n-l-1-i)!\\cdot(2\\cdot l+1+i)!}}$$\n",
      "\n",
      "$$\\hspace{20 mm} \\text{Where: }\\rho = \\frac{2 \\cdot z \\cdot r}{n \\cdot a_0}$$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def L(l,n,rho):\n",
      "    \"\"\"Laguerre polynomial\"\"\"\n",
      "    _L = 0.\n",
      "    for i in range((n-l-1)+1): #using a loop to do the summation \n",
      "        _L += ((-i)**i*fac(n+l)**2.*rho**i)/(fac(i)*fac(n-l-1.-i)*\\\n",
      "                                          fac(2.*l+1.+i))\n",
      "    return _L\n",
      "\n",
      "def R(r,n,l,z=1.,a_0=1.):\n",
      "    \"\"\"Radial function\"\"\"\n",
      "    rho = 2.*z*r/(n*a_0)\n",
      "    _L = L(l,n,rho)\n",
      "    _R = (2.*z/(n*a_0))**(3./2.)*sqrt(fac(n-l-1.)/\\\n",
      "         (2.*n*fac(n+l)**3.))*exp(-z/(n*a_0)*r)*rho**l*_L\n",
      "    return _R"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$$\\psi_{nlm}(r,\\theta,\\phi) = R_{nl}(r)Y_{lm}(\\theta,\\phi)$$\n",
      "\n",
      "$$P = \\psi^2 r^2$$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def Psi(r,n,l,m,phi,theta,z=1,a_0=1):\n",
      "    \"\"\"Wavefunction\"\"\"\n",
      "    _Y = Y_l_m(l,m,phi,theta)\n",
      "    _R = R(r,n,l)\n",
      "    return _R*_Y\n",
      "\n",
      "def P(r,n,l,m,phi,theta):\n",
      "    \"\"\"Returns the symbolic equation probability of the location \n",
      "    of an electron\"\"\"\n",
      "    return Psi(r,n,l,m,phi,theta)**2*r**2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Orbital Plotting Functions"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "r_fun = lambda _x,_y,_z: (np.sqrt(_x**2+_y**2+_z**2))\n",
      "theta_fun = lambda _x,_y,_z: (np.arccos(_z/r_fun(_x,_y,_z)))\n",
      "phi_fun = lambda _x,_y,_z: (np.arctan(_y/_x)*(1+_z-_z))\n",
      "\n",
      "def display_orbital(n,l,m_,no_of_contours = 16,Opaque=0.5):\n",
      "    \"\"\"Diplays a 3D view of electron orbitals\"\"\"\n",
      "    #The plot density settings (don't mess with unless you are sure)\n",
      "    rng = 12*n*1.5 #This determines the size of the box \n",
      "    _steps = 55j#           (it needs to be bigger with n).\n",
      "    _x,_y,_z = np.ogrid[-rng:rng:_steps,-rng:rng:_steps,-rng:rng:_steps]\n",
      "    \n",
      "    #Plot tweaks\n",
      "    color = (0,1.0,1.0) #relative RGB color (0-1.0 vs 0-255)\n",
      "    mlab.figure(bgcolor=color) #set the background color of the plot\n",
      "    \n",
      "    \n",
      "    P_tex = \"\" #initialize the LaTex string of the probabilities\n",
      "    \n",
      "    #Validate the quantum numbers\n",
      "    assert(n>=1), \"n must be greater or equal to 1\"       #validate the value of n\n",
      "    assert(0<=l<=n-1), \"l must be between 0 and n-1\"      #validate the value of l\n",
      "    assert(-l<=max(m_)<=l), \"p must be between -l and l\"  #validate the value of p\n",
      "    assert(-l<=min(m_)<=l), \"p must be between -l and l\"  #validate the value of p\n",
      "    \n",
      "        \n",
      "    for m in m_:\n",
      "        #Determine the probability equation symbolically and convert\n",
      "        #it to a string\n",
      "        prob = lambdastr((radius,angle_phi,angle_theta), P(radius,n,l,m,\n",
      "                                                           angle_phi,\n",
      "                                                           angle_theta))\n",
      "        \n",
      "        #record the probability equation as a LaTex string\n",
      "        P_eq = simplify(P(r,n,l,m,phi,theta))\n",
      "        P_tex+=\"$$P =\"+latex(P_eq)+\"$$ \\n\\n \" \n",
      "        \n",
      "        \n",
      "        #print(\"prob before substitution = \\n\\n\".format(prob)) #for debugging\n",
      "        \n",
      "        if '(nan)' in prob: #Check for errors in the equation\n",
      "            print(\"There is a problem with the probability function.\")\n",
      "            raise ValueError\n",
      "        \n",
      "        #Convert the finctions in the probability equation from the sympy  \n",
      "        #library to the numpy library to allow for the use of matrix \n",
      "        #calculations\n",
      "        prob = prob.replace('sin','np.sin') #convert to numpy\n",
      "        prob = prob.replace('cos','np.cos') #convert to numpy\n",
      "        prob = prob.replace('Abs','np.abs') #convert to numpy\n",
      "        prob = prob.replace('pi','np.pi')   #convert to numpy\n",
      "        prob = prob.replace('exp','np.exp') #convert to numpy\n",
      "        \n",
      "        #print(\"prob after substitution = \\n\\n\".format(prob)) #for debugging\n",
      "        \n",
      "        #convert the converted string to a callable function\n",
      "        Prob = eval(prob)\n",
      "        \n",
      "        #generate a set of data to plot the contours of.\n",
      "        w = Prob(r_fun(_x,_y,_z),phi_fun(_x,_y,_z),theta_fun(_x,_y,_z))\n",
      "        \n",
      "        #add the generated data to the plot\n",
      "        mlab.contour3d(w,contours=no_of_contours,opacity = Opaque, transparent=True)\n",
      "    \n",
      "    mlab.colorbar()\n",
      "    mlab.outline()\n",
      "    mlab.show() #this pops up a interactive window that allows you to \n",
      "    #            rotate the view\n",
      "    \n",
      "\n",
      "    #Information used for the 2D slices below\n",
      "    limits = []\n",
      "    lengths = []\n",
      "    for cor in (_x,_y,_z):\n",
      "        limit = (np.min(cor),np.max(cor))\n",
      "        limits.append(limit)\n",
      "        #print(np.size(cor))\n",
      "        lengths.append(np.size(cor))\n",
      "        #print(limit)\n",
      "    return (limits, lengths, _x, _y, _z, P_tex)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###Displaying the Orbitals:\n",
      "\n",
      "To display the orbital(s), execute the cell below .\n",
      "\n",
      "Notes on the quantum numbers:\n",
      "\n",
      "* $n$ is greater than or equal to 1\n",
      "* $l$ falls within the inclusive range of zero to $n - 1$\n",
      "* $m$ is within the range of negative $l$ to positive $l$\n",
      "\n",
      "[(Example values from wikipedia)](http://en.wikipedia.org/wiki/Atomic_orbital#Orbitals_table)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#    Set the quantum numbers for the orbitals (all in one spot)\n",
      "import warnings # in order to suppress divide_by_zero warnings...\n",
      "\n",
      "print(\"n must be greater or equal to 1.\")\n",
      "n = int(raw_input(\"Entry the quantum number for n = \"))\n",
      "\n",
      "print(\"\")\n",
      "l_str = raw_input(\"Enter a value for l such that it is less than n (default l=n-1) l = \")\n",
      "if l_str==\"\":\n",
      "    l=n-1\n",
      "else:\n",
      "    l = int(l_str)\n",
      "\n",
      "print(\"\\nThe next value, m, determines which specific orbital will be displayed.\")\n",
      "print(\"Enter a value(s) for m such that -l <= m <= l.\\n\"+\\\n",
      "      \"m can be a single number for a single orbital or a range for multiple.\")\n",
      "m_str = raw_input(\"Enter a number like, 2, or a range like, -2, 2.  m = \")\n",
      "if \",\" in m_str:\n",
      "    _m = eval(\"(\"+m_str+\")\")\n",
      "    m_ = range(_m[0],_m[1]+1,1)\n",
      "else:\n",
      "    m_ = [int(m_str)]\n",
      "\n",
      "print(\"\\nElectron orbitals are traditionally displayed at a 95% confidence interval.  \")\n",
      "print(\"The isosurface you would see is at a P value that depends on the principal \")\n",
      "print(\"quantum number and the shape of the orbital.  They are analogous to the height \")\n",
      "print(\"on a normal probability density function plot.  In displaying this surface \")\n",
      "print(\"the mayavi library is picking the confidence interval value for you, however \")\n",
      "print(\"some control can be had by setting number of isosuface contours.  \")\n",
      "print\n",
      "print(\"I have found that 16 is a good place to start, however on older computers there \")\n",
      "print(\"may be a problem rendering more than 7.\")\n",
      "n_o_c = raw_input(\"\\nEnter the number of isosurface contours to be displayed:[Default = 16] \")\n",
      "if n_o_c==\"\":\n",
      "    n_o_c = 16\n",
      "else:\n",
      "    n_o_c = abs(int(n_o_c))\n",
      "print(\"\\nIn order to see the various probability surfaces you can set the opacity of the \")\n",
      "print(\"plot from 0 to 1\")\n",
      "opacity = raw_input(\"Enter the opacity of the orbital plot:[Range 0 - 1, Default = 0.5] \")\n",
      "if opacity==\"\":\n",
      "    opacity = 0.5\n",
      "else:\n",
      "    opacity = abs(float(opacity))\n",
      "with warnings.catch_warnings():\n",
      "    warnings.simplefilter(\"ignore\")\n",
      "    limits, lengths, _x, _y, _z, P_tex = display_orbital(n,l,m_,n_o_c,opacity)\n",
      "\n",
      "txt = r\"$$\\textbf{The symbolic expression for the resulting probability equation is:}$$ \"\n",
      "Latex(txt+P_tex)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "n must be greater or equal to 1.\n"
       ]
      },
      {
       "name": "stdout",
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Entry the quantum number for n = 3\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "name": "stdout",
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Enter a value for l such that it is less than n (default l=n-1) l = 2\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "The next value, m, determines which specific orbital will be displayed.\n",
        "Enter a value(s) for m such that -l <= m <= l.\n",
        "m can be a single number for a single orbital or a range for multiple.\n"
       ]
      },
      {
       "name": "stdout",
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Enter a number like, 2, or a range like, -2, 2.  m = 0\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Electron orbitals are traditionally displayed at a 95% confidence interval.  \n",
        "The isosurface you would see is at a P value that depends on the principal \n",
        "quantum number and the shape of the orbital.  They are analogous to the height \n",
        "on a normal probability density function plot.  In displaying this surface \n",
        "the mayavi library is picking the confidence interval value for you, however \n",
        "some control can be had by setting number of isosuface contours.  \n",
        "\n",
        "I have found that 16 is a good place to start, however on older computers there \n",
        "may be a problem rendering more than 7.\n"
       ]
      },
      {
       "name": "stdout",
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Enter the number of isosurface contours to be displayed:[Default = 16] \n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "In order to see the various probability surfaces you can set the opacity of the \n",
        "plot from 0 to 1\n"
       ]
      },
      {
       "name": "stdout",
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Enter the opacity of the orbital plot:[Range 0 - 1, Default = 0.5] \n"
       ]
      },
      {
       "latex": [
        "$$\\textbf{The symbolic expression for the resulting probability equation is:}$$ $$P =\\frac{120^{1.0} r^{6}}{\\pi} 2.11688597605379 \\cdot 10^{-7} \\left(3 \\cos^{2}{\\left (\\theta \\right )} - 1\\right)^{2} e^{- 0.666666666666667 r}$$ \n",
        "\n",
        " "
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 19,
       "text": [
        "<IPython.core.display.Latex at 0x9ae3e10>"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Probability Equations:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Because the probability equations are solved symbolically we can have the additional benefit of seeing them expressed as equations. \n",
      "\n",
      "For example when $n=2$, with a little simplification, we get the following probability functions: \n",
      "\n",
      "When m is entered as -1 we have:\n",
      "$$\\hspace{50 mm} P = \\frac{r^{4} e^{- r} \\sin^{2}{\\left (\\phi \\right )} \\sin^{2}{\\left (\\theta \\right )}}{32 \\pi}$$ \n",
      "\n",
      "\n",
      "When m is entered as 0 we have:\n",
      "$$\\hspace{50 mm} P = \\frac{r^{4} e^{- r} \\cos^{2}{\\left (\\theta \\right )}}{32 \\pi}$$ \n",
      " \n",
      "\n",
      "When m is entered as 1 we have:\n",
      "$$\\hspace{50 mm} P = \\frac{r^{4} e^{- r} \\sin^{2}{\\left (\\theta \\right )} \\cos^{2}{\\left (\\phi \\right )}}{32 \\pi}$$ \n",
      "\n",
      "\n",
      "Execute the cell below to see the LaTex code for your probability equation."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Uncomment the line below to see the LaTex probability functions\n",
      "print(P_tex)\n",
      "# Latex(P_tex)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "$$P =\\frac{120^{1.0} r^{6}}{\\pi} 2.11688597605379 \\cdot 10^{-7} \\left(3 \\cos^{2}{\\left (\\theta \\right )} - 1\\right)^{2} e^{- 0.666666666666667 r}$$ \n",
        "\n",
        " \n"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Phase Information (2D Slices)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The expression of the probability equation - specifically, taking the square of the wavefunction - leads to a loss of the phase information of the wavefunction.  As visualized in the animation of a d-orbital (see below), we can examine the phase information in a 2D representation."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "![Wikipedia](http://upload.wikimedia.org/wikipedia/commons/6/6f/Drum_vibration_mode22.gif)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In order to retain the phase information, the mathematical treatment needs to be different, which we elaborate on below.  \n",
      "\n",
      "####Run the cell below once to define the functions needed for a 2D slice."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import matplotlib.pyplot as plt\n",
      "\n",
      "def Y_l_m_signed(l,m,phi,theta):\n",
      "    \"\"\"Signed spherical harmonics\"\"\"\n",
      "    eq = P_l_m(m,l,theta)\n",
      "    if m>0:\n",
      "        pe=re(exp(I*m*phi))*sqrt(2)\n",
      "    elif m<0:\n",
      "        pe=im(exp(I*m*phi))*sqrt(2)\n",
      "    elif m==0:\n",
      "        pe=1\n",
      "    return sqrt(((2*l+1)*fac(l-Abs(m)))/(4*pi*fac(l+Abs(m))))*pe*eq\n",
      "\n",
      "def Psi_signed(r,n,l,m,phi,theta,z=1,a_0=1):\n",
      "    \"\"\"Signed wave function \"\"\"\n",
      "    _Y = Y_l_m_signed(l,m,phi,theta)\n",
      "    _R = R(r,n,l)\n",
      "    return _R*_Y\n",
      "\n",
      "def signed_P(r,n,l,m,phi,theta):\n",
      "    \"\"\"Returns the symbolic equation probability of the location \n",
      "    of an electron with the phase information included\"\"\"\n",
      "    result = Psi_signed(r,n,l,m,phi,theta)**3*r**2/abs(Psi_signed(r,n,l,m,phi,theta))\n",
      "    return result\n",
      "\n",
      "def signed_prob(m):\n",
      "    \"\"\"Returns a callable signed probability function that can be \n",
      "    used to plot 2D slices and probability amplitude vs radius.\"\"\"\n",
      "    #Determine the probability equation symbolically and convert\n",
      "    #it to a string \n",
      "        \n",
      "    ##(THIS SHOULD BE SIGNED [+ OR -])##\n",
      "        \n",
      "    prob = lambdastr((radius,angle_phi,angle_theta), signed_P(radius,\n",
      "                                                              n,l,m,\n",
      "                                                              angle_phi,\n",
      "                                                              angle_theta))\n",
      "        \n",
      "    #record the probability equation as a LaTex string\n",
      "    P_eq = simplify(P(r,n,l,m,phi,theta))\n",
      "        \n",
      "    #print(\"prob before substitution = \\n\\n\".format(prob)) #for debugging\n",
      "        \n",
      "    if '(nan)' in prob: #Check for errors in the equation\n",
      "        print(\"There is a problem with the probability function.\")\n",
      "        raise ValueError\n",
      "        \n",
      "    #Convert the finctions in the probability equation from the sympy  \n",
      "    #library to the numpy library to allow for the use of matrix \n",
      "    #calculations\n",
      "    prob = prob.replace('sin','np.sin') #convert to numpy\n",
      "    prob = prob.replace('cos','np.cos') #convert to numpy\n",
      "    prob = prob.replace('Abs','np.abs') #convert to numpy\n",
      "    prob = prob.replace('pi','np.pi')   #convert to numpy\n",
      "    prob = prob.replace('exp','np.exp') #convert to numpy\n",
      "        \n",
      "    #print(\"prob after substitution = \\n\\n{}\".format(prob)) #for debugging\n",
      "        \n",
      "    #convert the converted string to a callable function\n",
      "    Prob = eval(prob)\n",
      "    return Prob\n",
      "\n",
      "def orbital_plane(plane = \"xy\"):\n",
      "    \"\"\"Returns information values to display the cross sestional view of the orbitals\"\"\"\n",
      "    center = (np.max(length)-1)/2\n",
      "    if plane not in ['xy','yz','xz']:\n",
      "        er = \"The plane can only be 'xy', 'yz', or 'xz'\"\n",
      "        raise ValueError(er)\n",
      "    for m in m_:\n",
      "        Prob = signed_prob(m)\n",
      "               \n",
      "        #generate a set of data to plot the contours of.\n",
      "        w = Prob(r_fun(_x,_y,_z),phi_fun(_x,_y,_z),theta_fun(_x,_y,_z))\n",
      "        #print(plane)\n",
      "        if plane==\"xy\":\n",
      "            W=w[:,:,center]\n",
      "        elif plane == \"yz\":\n",
      "            W=np.array(w[center,:,:]).transpose()\n",
      "        elif plane == \"xz\":\n",
      "            W=np.array(w[:,center,:]).transpose()\n",
      "        na = W==np.nan\n",
      "        W[np.isnan(W)] = 0\n",
      "    return W, Prob\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 21
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Display the 2D slices"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The phase information of the orbital that was previously rendered in 3D will be displayed be executing the cell below."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
      "from matplotlib import rcParams\n",
      "%matplotlib inline\n",
      "rcParams.update({'font.size': 12, 'font.family': 'serif'})\n",
      "length=max(lengths)\n",
      "# print(length)\n",
      "x0,x1,y0,y1 = (-length/2,length/2)*2\n",
      "def demo():\n",
      "    #Figure sizes\n",
      "    fig_x = 12\n",
      "    fig_y = 24\n",
      "    \n",
      "    fig1 = plt.figure(1,figsize=(fig_x,fig_y))\n",
      "    ax=[]\n",
      "    for index, plane in enumerate(['xy','yz','xz']):\n",
      "        ax.append(fig1.add_subplot(3, 1, index+1))\n",
      "        ax[index].set_title('%s Plane'%plane)\n",
      "        ax[index].set_xlabel(plane[0])\n",
      "        ax[index].set_ylabel(plane[1])\n",
      "        result, Prob = orbital_plane(plane)\n",
      "        im = ax[index].imshow(result,origin='lower', \n",
      "                              extent=[x0,x1,y0,y1])\n",
      "        \n",
      "        plt.colorbar(im)\n",
      "        plt.tight_layout()\n",
      "\n",
      "    plt.draw()\n",
      "    plt.show()\n",
      "    return result\n",
      "\n",
      "with warnings.catch_warnings():\n",
      "    warnings.simplefilter(\"ignore\")\n",
      "    result = demo()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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2Kqfd5JmiSwiZa8yK2Q/+/d//HW95y1vw9a9/vWX8ySefxKpVq3D66afjoosu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zoqcRgCCkWQGK7oqTnKlk04ptv66c/bYqcriew4cW1VAbXpQAQFDvZhyzP1Gs95wjOe8lw95Tmv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\nZzCdTvH00093XrvrPjynTGqllPjzP/9zXHPNNdi/fz9e9rKX4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Pnmm+X7vq644godPnxY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\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DRV7tuAFjTZ9H+fOr1oUQQqxCUivEXqEqR00CVV0Fq5p6kG99mktbYHLZzablMtZj8tkM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\nJZlCHw85AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x9b48390>"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Probability Amplitude Plot"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Due to the inexact nature of plotting 3D contours it is useful to look at a plot of the probability amplitude in a simple plot as a function of distance from the center of the atom.  However, to do this we should restrict ourselves to a single value m for clarity.  We also have to pick a radial direction.  This is based on the angle from the positive $x$-axis is in the $xy$ plane, $\\phi$ (phi) and the angle from the positive $z$-axis, $\\theta$ (theta).  \n",
      "\n",
      "The radial direction will be the direction that the plot is done through the orbital cloud.  If the cloud is a s type orbital then the direction will not matter but with other orbitals the direction will make a great deal of difference in what is shown."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def display_prob_amplitude():\n",
      "    \"\"\"Displays the value of P from above as a plot\n",
      "    along a given angular direction as a function from \n",
      "    the center of the atom for a given value of m.\n",
      "    \"\"\"\n",
      "    #phi\n",
      "    print(\"We need to have a radial driection for the plot.  First Pick an\")\n",
      "    print(\"angle in the xy plane (phi) for the direction of the plot.\")\n",
      "    print(\"The default value is 0 but it could be anything from 0 up to 360.\")\n",
      "    phi_str = raw_input(\"phi = \")\n",
      "    phi_rad = 0 if phi_str==\"\" else np.deg2rad(float(phi_str))\n",
      "    #theta\n",
      "    print(\"We also need an angle from the z-axia (theta) for the plot.\")\n",
      "    print(\"The default value is 0 but it could be anything from 0 up to 360.\")\n",
      "    theta_str = raw_input(\"theta = \")\n",
      "    theta_rad = 0 if theta_str==\"\" else np.deg2rad(float(theta_str))\n",
      "     #m   \n",
      "    print(\"\\nThe next value, m, determines which specific orbital will be displayed.\")\n",
      "    print(\"Remember that l = %s\"%l_str)\n",
      "    m_str = raw_input(\"Enter a number such that -l <= m <= l,  m = \")\n",
      "    m = 0 if m_str==\"\" else [int(m_str)]\n",
      "    Prob = signed_prob(m)\n",
      "    rad_dis = np.array(range(0,55))*12*n*1.5j\n",
      "    p_amp = np.zeros(len(rad_dis))\n",
      "    real_rad = np.zeros(len(rad_dis))\n",
      "    for index, r in enumerate(rad_dis):\n",
      "        p_amp[index] = Prob(r,phi_rad,theta_rad)\n",
      "        real_rad[index] = r*1j\n",
      "#     print((np.size(rad_dis),len(p_amp)))\n",
      "    plt.plot(real_rad,p_amp)\n",
      "    return (real_rad,p_amp)\n",
      "\n",
      "rad_dis,p_amp=display_prob_amplitude()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "We need to have a radial driection for the plot.  First Pick an\n",
        "angle in the xy plane (phi) for the direction of the plot.\n",
        "The default value is 0 but it could be anything from 0 up to 360.\n"
       ]
      },
      {
       "name": "stdout",
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "phi = \n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "We also need an angle from the z-axia (theta) for the plot.\n",
        "The default value is 0 but it could be anything from 0 up to 360.\n"
       ]
      },
      {
       "name": "stdout",
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "theta = \n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "The next value, m, determines which specific orbital will be displayed.\n",
        "Remember that l = 2\n"
       ]
      },
      {
       "name": "stdout",
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Enter a number such that -l <= m <= l,  m = \n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "-c:27: ComplexWarning: Casting complex values to real discards the imaginary part\n",
        "-c:28: ComplexWarning: Casting complex values to real discards the imaginary part\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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bL+C+7PPll3IKRV8nfHFl4UL5QfLtt/IuWSIKTbrO/INV9gHU9fjxp+wTzMz/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\ngz8RUQRi8CciikAM/kREEYjBn4goAv0/6JLUnt4Zl7EAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb4a3d90>"
       ]
      }
     ],
     "prompt_number": 46
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(rad_dis)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.\n",
        "  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.\n",
        "  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.\n",
        "  0.]\n"
       ]
      }
     ],
     "prompt_number": 44
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(p_amp)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[  0.00000000e+00   1.02621449e+05   4.96444114e+07  -2.19533074e+08\n",
        "  -2.86156083e+09   7.49905595e+09   2.68642248e+10  -7.38013260e+10\n",
        "  -1.08855320e+11   3.89851719e+11   2.27508217e+11  -1.40272265e+12\n",
        "  -7.42459665e+10   3.85258498e+12  -1.35085287e+12  -8.56858339e+12\n",
        "   6.23992037e+12   1.58598825e+13  -1.83696085e+13  -2.44092244e+13\n",
        "   4.30639013e+13   2.97292797e+13  -8.63485555e+13  -2.24601895e+13\n",
        "   1.52961821e+14  -1.29704698e+13  -2.43060810e+14   9.85968002e+13\n",
        "   3.47773794e+14  -2.61243396e+14  -4.44168494e+14   5.28177904e+14\n",
        "   4.90673375e+14  -9.19628546e+14  -4.24410939e+14   1.43824448e+15\n",
        "   1.62167802e+14  -2.05632294e+15   3.93277322e+14   2.70250112e+15\n",
        "  -1.34011378e+15  -3.25048089e+15   2.75717626e+15   3.51305179e+15\n",
        "  -4.67695753e+15  -3.24501433e+15   7.05408491e+15   2.15840455e+15\n",
        "  -9.73305488e+15   4.74527863e+13   1.24206029e+16  -3.64014020e+15\n",
        "  -1.46692970e+16   8.79396479e+15   1.58794749e+16]\n"
       ]
      }
     ],
     "prompt_number": 41
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Appendix: (Other Examples)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example of Single Orbital using $n=3$, $l=2$, $m=0$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<a href=\"http://i.imgur.com/QM03swU\"><img src=\"http://i.imgur.com/QM03swU.png\" title=\"Hosted by imgur.com\" width=50% height=50% /></a>\n",
      "\n",
      "Variable values used:\n",
      "\n",
      "    n=3\n",
      "    l=2\n",
      "    m = 0\n",
      "    no_of_contours = 16\n",
      "    opacity = 1"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example of Single Orbital using $n=2$, $l=1$, $m=0$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<a href=\"http://i.imgur.com/NrISjZu\"><img src=\"http://i.imgur.com/NrISjZu.png\" title=\"Hosted by imgur.com\" width=50% height=50%/></a> \n",
      "\n",
      "Variable values used:\n",
      "\n",
      "    n=2\n",
      "    l=1\n",
      "    m = 0\n",
      "    no_of_contours = 16\n",
      "    opacity = 1"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example of Single Orbital using $n=4$, $l=3$, $m=-2$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<a href=\"http://i.imgur.com/3bfD25v\"><img src=\"http://i.imgur.com/3bfD25v.png\" title=\"Hosted by imgur.com\"  width=50% height=50%/></a>\n",
      "\n",
      "Variable values used:\n",
      "\n",
      "    n=4\n",
      "    l=3\n",
      "    m = -2\n",
      "    no_of_contours = 16\n",
      "    opacity = 1"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Example Output using $n=8$, $l=7$, $m= -7 \\text{, } 7$ "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<a href=\"http://i.imgur.com/YGwBxeU\"><img src=\"http://i.imgur.com/YGwBxeU.png\" title=\"Hosted by imgur.com\" height=50% width=50%/></a>\n",
      "\n",
      "Variable values used:\n",
      "\n",
      "    n=8\n",
      "    l=7\n",
      "    m = -7, 7\n",
      "    no_of_contours = 16\n",
      "    opacity = 1"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Appendix: (Future Work)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Adding functions that plot the probability amplitude of orbitals as seen [here](http://faculty.pingry.org/dburns/chemistry/documents/ProbabilityAmplitudeofs-Orbitals.pdf)."
     ]
    }
   ],
   "metadata": {}
  }
 ]
}