 
Construction of the Electronic Angular Wave Functions and Probability Distributions of the Hydrogen Atom©  
Mark David Ellison Wittenberg University P. O. Box 720 Springfield, OH 45501 United States mail to: mellison@wittenberg.edu  
Thomas S Kuntzelman Department of Chemistry Spring Arbor University Spring Arbor, MI 49283 United States mail to: tkuntzle@arbor.edu  
John Tippin Deparment of Mathematics Spring Arbor University Spring Arbor, MI 49283 United States  
Abstract  
This Mathcad document allows students to explore the characteristics of the components of the angular electronic wave function of the hydrogen atom,Y_{l}^{m}(θ, φ). Within this exercise, Y_{l}^{m}(θ, φ) is separated into three parts: a normalization constant, a polynomial function and an exponential function. After choosing quantum numbers l and m, users can evaluate graphically display the component functions of Y_{l}^{m}(θ, φ) separately. After combining these components, the entire wave function is constructed and a graph of its associated probability density is displayed. Users have the opportunity to discover when, why and how linear combinations of the exponential portion of Y_{l}^{m}(θ, φ) are used in constructing orbital plots that are normally displayed in textbooks. In addition, students gain a mathematical understanding of why the quantum number m can only vary from l to l. This document illustrates a method by which one may generate and present graphs of the probability distributions of the angular electronic wave function for the hydrogen atom "from scratch". No attempt is made to derive this wave function.  
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©Copyright 2007 Journal of Chemical Education  