 
Construction of the Electronic Radial Wave Functions and Probability Distributions of Hydrogenlike Systems©  
Thomas S Kuntzelman Department of Chemistry Spring Arbor University Spring Arbor, MI 49283 United States mail to: tkuntzle@arbor.edu  
Abstract  
This Mathcad document allows users to explore the characteristics of the components of the radial electronic wave function of the hydrogen atom, R(r) (where r is the distance of the electron from the nucleus). Within this exercise, R(r) is separated into four parts: a normalization constant, a polynomial function of r, an associated Laguerre polynomial of r, and an exponential function of r. After choosing quantum numbers n and l, users can evaluate graphically display the component functions of R(r) separately. After combining these components, the entire wave function is constructed and graphs of R(r) and its associated probability density are displayed. How each separate function of r affects the overall radial wave function can be investigated. Finally, users have an opportunity to discover some relationships between values of n, l and certain properties of the radial electronic wave function and its associated probability density (such as the number of nodes and the most probable distance from the nucleus).  
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Comments to: tkuntzle@arbor.edu  
©Copyright 2007 Journal of Chemical Education  