{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "#### Hydrogen Atomic Orbitals\n", "\n", "This document is a Jupyter notebook. If this is the first time you've worked with one, please take a moment to briefly read [these instructions](https://jupyter-notebook.readthedocs.io/en/stable/notebook.html#structure-of-a-notebook-document) explaining how to use it. In particular, make sure you understand the difference between a Markdown cell used for text/images/equations (such as the current one) and a code cell, which executes python code. When you do problem sets in this course, you will be expected to submit Jupyter Notebook files that have a mix of explanatory text and working code.\n", "\n", "In this notebook, we will be visualizing the atomic orbitals of the hydrogen atom and learning about code vectorization along the way. Before starting, you should have reviewed the [Week 2 Background](https://leeping.github.io/che155/weeks/2.html). The equation for a hydrogen atomic orbital is\n", "\n", "$$ \\psi_{n\\ell m}(r,\\theta,\\phi) = \\sqrt{ \\left( \\frac{2}{n} \\right)^3 \\frac{ (n-\\ell-1)! }{2n[(n+\\ell)!]^3} } e^{-r/n} \\left(\\frac{r}{n}\\right)^\\ell L^{2\\ell+1}_{n-\\ell-1}(r) Y_\\ell^m(\\theta,\\phi) $$\n", "\n", "using spherical coordinates defined as\n", "\n", "