Lecture2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "funded-mandate",
   "metadata": {},
   "source": [
    "# Lecture 2\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "representative-bargain",
   "metadata": {},
   "source": [
    "# Click on a cell, Shift+Enter to run the cell"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "classified-housing",
   "metadata": {},
   "source": [
    "**Demo** Plot the energy of Hydrogen atom in Rutherford's model as a function of the radius r"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "three-battle",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.constants as const"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "competitive-distinction",
   "metadata": {},
   "outputs": [],
   "source": [
    "# A series of r in the range from 1e-15 m (1e-5 angstrom) to 1e-9 m (10 angstrom), evenly distributed in the log scale\n",
    "r = np.logspace(np.log10(1e-13),np.log10(1e-9), num=1000, endpoint=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "desperate-encyclopedia",
   "metadata": {},
   "outputs": [],
   "source": [
    "E=-0.5*1/(4*const.pi*const.epsilon_0)*const.e/r"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "favorite-slovak",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# size of the figure in inches\n",
    "plt.figure(figsize=(4,4))\n",
    "\n",
    "# Plot the rho functions\n",
    "plt.plot(r,E,label=r'$E(r)$')\n",
    "\n",
    "# set plot limits\n",
    "#plt.ylim(min(min(rho_T1),min(rho_T2)), max(max(rho_T1),max(rho_T2)))\n",
    "#plt.xlim(1e4,1e20)\n",
    "plt.xscale('log')\n",
    "\n",
    "# Add a title\n",
    "plt.title(r'Energy of hydrogen atom in Rutherford model')\n",
    "\n",
    "# Add X and y Label\n",
    "plt.xlabel(r'$r$ (m)')\n",
    "plt.ylabel(r'$E$ (J)')\n",
    "\n",
    "# Add a grid\n",
    "plt.grid(alpha=.4,linestyle='--')\n",
    "\n",
    "# Add a Legend\n",
    "plt.legend()\n",
    "\n",
    "# Show the plot\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {
    "image-2.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "dying-straight",
   "metadata": {},
   "source": [
    "**Exercise 2.1** Calculate the energy of the state corresponding to n=1 in units of eV. 𝐸=−(𝑚_𝑒 𝑒^4)/(32𝑛^2 ℏ^2 𝜋^2 𝜖_0^2 ),𝑛=1,2,3,…\n",
    "![image-2.png](attachment:image-2.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "running-criminal",
   "metadata": {},
   "outputs": [],
   "source": [
    "E = -(const.m_e*const.e**4)/(32*const.hbar**2*const.pi**2*const.epsilon_0**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "important-desert",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-2.179872361086218e-18"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# In SI Unit (Joule)\n",
    "E"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "returning-burke",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.602176634e-19"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 1eV = ? J\n",
    "eV = const.e*1\n",
    "eV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "prescribed-competition",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-13.605693122885839"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "E/eV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "valid-blake",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2187691.2636364764"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "const.e**2/(4*const.pi*const.epsilon_0*const.hbar)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "median-customs",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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   "language": "python",
   "name": "conda-env-notebook-py"
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  "language_info": {
   "codemirror_mode": {
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   "file_extension": ".py",
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