{
 "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 (\n",
    "        2**-0.5 * np.exp(t * 1j) * np.sin(np.pi * x)\n",
    "        + 0.5 * np.exp(t * 4j) * np.sin(2 * np.pi * x)\n",
    "        + 0.5 * np.exp(t * 9j) * np.sin(3 * np.pi * x)\n",
    "    )\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=ax)\n",
    "block2 = amp.blocks.Line(X, Y2, ax=ax)\n",
    "\n",
    "anim = amp.Animation([block1, block2], timeline)\n",
    "\n",
    "# Your standard matplotlib stuff\n",
    "plt.title(\n",
    "    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",
    ")\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",
  "kernelspec": {
   "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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 "nbformat": 4,
 "nbformat_minor": 2
}