{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Square Well"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.animation import PillowWriter\n",
    "import animatplot as amp\n",
    "\n",
    "\n",
    "def psi(x, t):\n",
    "    return (2**-.5*np.exp(t*1j)*np.sin(np.pi*x)\n",
    "            + .5*np.exp(t*4j)*np.sin(2*np.pi*x)\n",
    "            + .5*np.exp(t*9j)*np.sin(3*np.pi*x))\n",
    "\n",
    "\n",
    "x = np.linspace(0, 1, 20)\n",
    "t = np.linspace(0, 10, 20)\n",
    "\n",
    "X, T = np.meshgrid(x, t)\n",
    "Y1 = psi(X, T).real\n",
    "Y2 = psi(X, T).imag\n",
    "\n",
    "timeline = amp.Timeline(t, 's', 24)\n",
    "\n",
    "ax = plt.axes(xlim=[0, 1], ylim=[-2, 2])\n",
    "block1 = amp.blocks.Line(X, Y1, ax)\n",
    "block2 = amp.blocks.Line(X, Y2, ax)\n",
    "\n",
    "anim = amp.Animation([block1, block2], timeline)\n",
    "\n",
    "# Your standard matplotlib stuff\n",
    "plt.title(r'Particle in a Box: $|\\Psi\\rangle = \\frac{1}{\\sqrt{2}}'\n",
    "          r'|E_1\\rangle + \\frac{1}{2}|E_2\\rangle + \\frac{1}{2}|E_3\\rangle$',\n",
    "          y=1.03)\n",
    "plt.xlabel('position')\n",
    "plt.ylabel(r'$\\Psi$')\n",
    "plt.legend(['Real', 'Imaginary'])\n",
    "\n",
    "anim.toggle()\n",
    "anim.timeline_slider()\n",
    "\n",
    "anim.save('sq_well.gif', writer=PillowWriter(fps=5))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    ".. image:: sq_well.gif"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Raw Cell Format",
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   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
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