SchrodingerEquation.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define constants\n",
    "L = 10.0  # Length of the box\n",
    "N = 1000  # Number of points\n",
    "x = np.linspace(0, L, N)  # x values\n",
    "dx = x[1] - x[0]  # Difference between successive x values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the Laplacian operator as a matrix\n",
    "Laplacian = (-2.0*np.diag(np.ones(N)) + np.diag(np.ones(N-1),1) + np.diag(np.ones(N-1),-1)) / (dx**2)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the Hamiltonian operator\n",
    "Hamiltonian = -(1/2) * Laplacian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Compute the eigenvalues and eigenvectors\n",
    "eigenvalues, eigenvectors = np.linalg.eig(Hamiltonian)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Sort the eigenvalues and eigenvectors\n",
    "sorted_indices = np.argsort(eigenvalues)\n",
    "eigenvalues = eigenvalues[sorted_indices]\n",
    "eigenvectors = eigenvectors[:, sorted_indices]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the lowest few energy levels\n",
    "for i in range(4):\n",
    "    plt.plot(x, eigenvectors[:, i] + eigenvalues[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Particle in a Box\")\n",
    "plt.xlabel(\"Position\")\n",
    "plt.ylabel(\"Energy\")\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "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": "3.9.0"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}