'cookbook added'

_toc.yml

@@ -75,7 +75,7 @@ parts:
     - file: ch08/note09
     - file: ch08/demo_h2plus
   - file: scratch
-  - file: units
+  - file: cookbook
   - file: overview
 
 - caption: Extra stuff

cookbook.ipynb

@@ -0,0 +1,141 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Cookbook: Using python to tame the math"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np  \n",
+    "import matplotlib.pyplot as plt\n",
+    "from ipywidgets import interact\n",
+    "import scipy  \n",
+    "from scipy.constants import physical_constants, hbar, h, c, k, m_e, Rydberg, e, N_A\n",
+    "\n",
+    "%matplotlib inline\n",
+    "%config InlineBackend.figure_format='retina'"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Example-1\n",
+    "\n",
+    "- Show that wavefunctions $f_1 = sin(x)$ and $f_2=cos(x)$ are orthogonal on $(0, 2\\pi)$ interval."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "#### Numerical solution"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "\n",
+    "# Define the range of x values\n",
+    "x = np.linspace(0, 2 * np.pi, 1000)\n",
+    "\n",
+    "# Calculate sin(x) and cos(x)\n",
+    "y_sin = np.sin(x)\n",
+    "y_cos = np.cos(x)\n",
+    "\n",
+    "# Calculate the numerical integral (dot product)\n",
+    "dot_product = np.trapz(y_sin * y_cos, x)\n",
+    "\n",
+    "# Print the result\n",
+    "print(f\"The numerical integral (dot product) of sin(x) * cos(x) over [0, 2π] is approximately: {dot_product:.4f}\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "#### Symbolic solution"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "import sympy as sp\n",
+    "\n",
+    "# Define the symbolic variable\n",
+    "x = sp.symbols('x')\n",
+    "\n",
+    "# Define sin(x) and cos(x)\n",
+    "sin_x = sp.sin(x)\n",
+    "cos_x = sp.cos(x)\n",
+    "\n",
+    "# Calculate the symbolic integral of sin(x) * cos(x) over [0, 2π]\n",
+    "integral = sp.integrate(sin_x * cos_x, (x, 0, 2 * sp.pi))\n",
+    "\n",
+    "# Print the result\n",
+    "print(f\"The symbolic integral of sin(x) * cos(x) over [0, 2π] is: {integral}\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "#### Visual solution"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "def plot_orthogonality():\n",
+    "\n",
+    "    # Define the range of x values\n",
+    "    x = np.linspace(0, 2 * np.pi, 1000)\n",
+    "    \n",
+    "    # Calculate sin(x) and cos(x)\n",
+    "    y_sin = np.sin(x)\n",
+    "    y_cos = np.cos(x)\n",
+    "    \n",
+    "    # Plotting sin(x) and cos(x)\n",
+    "    plt.plot(x, y_sin, label='sin(x)')\n",
+    "    plt.plot(x, y_cos, label='cos(x)')\n",
+    "    \n",
+    "    # Fill the area between two horizontal curves\n",
+    "    plt.fill_between(x, y_sin * y_cos, alpha=0.3, color='gray', label='sin(x) * cos(x)')\n",
+    "    \n",
+    "    # Labels and title\n",
+    "    plt.xlabel('x')\n",
+    "    plt.ylabel('Function Value')\n",
+    "    plt.title('Orthogonality of sin(x) and cos(x)')\n",
+    "    plt.legend()\n",
+    "    plt.grid(True)\n",
+    "    plt.show()\n",
+    "\n",
+    "# Call the function\n",
+    "plot_orthogonality()"
+   ]
+  }
+ ],
+ "metadata": {
+  "language_info": {
+   "name": "python"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

overview.md

@@ -1,4 +1,29 @@
 # Equation sheet
+
+## Units
+
+### Constants
+| Energy Constant | Value |
+|:----------------|--------------------:|
+| $h = 6.63 \cdot 10^{-34} \, [J \cdot s]$ | $m_u = 1.66 \cdot 10^{-27} \, [kg]$ |
+| $k_B = 1.38 \cdot 10^{-23} \, [J \cdot K^{-1}]$ | $N_A = 6.02 \cdot 10^{23} \, [mol^{-1}]$ |
+| $c = 3.0 \cdot 10^{8} \, [m \cdot s^{-1}]$ | $m_e = 9.1093837015 \cdot 10^{-31} \, [kg]$ |
+| $R_H = 109680 \, [cm^{-1}]$ | $e = 1.602176634 \cdot 10^{-19} \, [C]$ |
+
+
+### Energy Unit Converter
+
+- See [here](https://www.weizmann.ac.il/oc/martin/tools/hartree.html) for an interactive option.
+
+| Unit | $J$ | $eV$ | $cm^{-1}$ | $hartree$ | $Hz$ |
+|:----:|:---:|:----:|:---------:|:---------:|:----:|
+| $J$ | $1$ | $6.24181 \cdot 10^{18}$ | $5.03445 \cdot 10^{22}$ | $2.294 \cdot 10^{17}$ | $1.50930 \cdot 10^{33}$ |
+| $eV$ | $1.60210 \cdot 10^{-19}$ | $1$ | $8065.73$ | $0.0367502$ | $2.41804 \cdot 10^{14}$ |
+| $cm^{-1}$ | $1.98630 \cdot 10^{-23}$ | $1.23981 \cdot 10^{-4}$ | $1$ | $4.55633 \cdot 10^{-6}$ | $2.99793 \cdot 10^{10}$ |
+| $hartree$ | $43.60 \cdot 10^{-19}$ | $27.2107$ | $219474.63$ | $1$ | $6.57966 \cdot 10^{15}$ |
+| $Hz$ | $6.62561 \cdot 10^{-34}$ | $4.13558 \cdot 10^{-15}$ | $3.33565 \cdot 10^{-11}$ | $1.51983 \cdot 10^{-16}$ | $1$ |
+
+
 ## From classical to Quantum 
 
 ### Blackbody radiation