101- 2D double slit experiment .ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "source": [
    "%matplotlib ipympl\r\n",
    "import numpy as np\r\n",
    "from qmsolve import Hamiltonian, SingleParticle, TimeSimulation, init_visualization, femtoseconds, m_e, Å"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "source": [
    "#=========================================================================================================#\r\n",
    "#First, we define the Hamiltonian of a single particle confined in an harmonic oscillator potential. \r\n",
    "#=========================================================================================================#\r\n",
    "\r\n",
    "#interaction potential\r\n",
    "def double_slit(particle): \r\n",
    "    \"\"\"define double slit as as an interactive potential: returns 0 for slit opening and 1 for rest of wall\"\"\"\r\n",
    "    b = 2.0* Å # slits separation\r\n",
    "    a = 0.5* Å # slits width\r\n",
    "    d = 0.5* Å # slits depth\r\n",
    "\r\n",
    "    return np.where( ((particle.x < - b/2 - a) | (particle.x > b/2 + a) | ((particle.x > -b/2)  \r\n",
    "                     & (particle.x < b/2))) & ((particle.y < d/2) & (particle.y > -d/2) ),  1e5,  0)\r\n",
    "\r\n",
    "#build the Hamiltonian of the system\r\n",
    "H = Hamiltonian(particles = SingleParticle(m = m_e), \r\n",
    "                potential = double_slit, \r\n",
    "                spatial_ndim = 2, N = 256, extent = 30 * Å)\r\n",
    "\r\n",
    "#=========================================================================================================#\r\n",
    "# Define the wavefunction at t = 0  (initial condition)\r\n",
    "#=========================================================================================================#\r\n",
    "\r\n",
    "def initial_wavefunction(particle):\r\n",
    "    #This wavefunction correspond to a gaussian wavepacket with a mean Y momentum equal to p_y0\r\n",
    "    σ = 1.0 * Å\r\n",
    "    v0 = 80 * Å / femtoseconds\r\n",
    "    p_y0 = m_e * v0\r\n",
    "    return np.exp( -1/(4* σ**2) * ((particle.x-0)**2+(particle.y+8* Å)**2)) / np.sqrt(2*np.pi* σ**2)  *np.exp(p_y0*particle.y*1j)\r\n",
    "\r\n"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "source": [
    "#=========================================================================================================#\r\n",
    "# Set and run the simulation\r\n",
    "#=========================================================================================================#\r\n",
    "\r\n",
    "\r\n",
    "total_time = 0.2 * femtoseconds\r\n",
    "sim = TimeSimulation(hamiltonian = H, method = \"split-step\")\r\n",
    "sim.run(initial_wavefunction, total_time = total_time, dt = total_time/8000., store_steps = 800)\r\n",
    "\r\n",
    "\r\n"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stderr",
     "text": [
      "\n"
     ]
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Took 149.14500260353088\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "source": [
    "#=========================================================================================================#\r\n",
    "# Finally, we visualize the time dependent simulation\r\n",
    "#=========================================================================================================#\r\n",
    "\r\n",
    "visualization = init_visualization(sim)\r\n",
    "\r\n",
    "visualization.animate(xlim=[-15* Å,15* Å], ylim=[-15* Å,15* Å], save_animation=True,\r\n",
    "                            potential_saturation = 0.5, wavefunction_saturation = 0.2,\r\n",
    "                             animation_duration = 10, fps = 30)\r\n"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "3ee1b2818fc24ae588e7bf93a6746990"
      },
      "image/png": "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",
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {}
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "source": [
    "# To create a GIF\r\n",
    "import os\r\n",
    "if os.path.isfile(\"animation.gif\"):\r\n",
    "\tos.remove(\"animation.gif\")\r\n",
    "# For output representing on notebook\r\n",
    "import ffmpy\r\n",
    "ff = ffmpy.FFmpeg(\r\n",
    "\tinputs = {\"animation.mp4\" : None},\r\n",
    "\toutputs = {\"animation.gif\" : None})\r\n",
    "\r\n",
    "ff.run()"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "(None, None)"
      ]
     },
     "metadata": {},
     "execution_count": 7
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "<img src=\"animation.gif\" width=\"750\" >"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "source": [
    "\r\n",
    "# os.remove(\"animation.mp4\")\r\n",
    "# os.remove(\"animation.gif\")"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Inspired by and referenced from https://github.com/quantum-visualizations/qmsolve/tree/main/qmsolve"
   ],
   "metadata": {}
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "42586e27f6d94440f72033f095fd9a88b523b0c572b7a3ee68dfb7c6d424936a"
  },
  "kernelspec": {
   "name": "python3",
   "display_name": "Python 3.7.9 64-bit ('base': conda)"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}