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  Home > JCE Print > Journal of Chemical Education > Issues > 2007  > July  >
Information • Textbooks • Media • Resources
JCE SymMath: Symbolic Mathematics in Chemistry
Construction of the Electronic Radial Wave Functions and Probability Distributions of Hydrogen-like Systems
Thomas S. Kuntzleman
Department of Chemistry, Spring Arbor University, Spring Arbor MI 49283
Cover
July 2007
Vol. 84 No. 7
p. 1231
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 and 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).

The First 5 Laguerre Polynomials
Supplement
Fully interactive computer algebra files are available in the JCE SymMath collection of the JCE Digital Library Only@JCE Online.
More Information
*
Citation
Kuntzleman, Thomas S. J. Chem. Educ. 2007, 84, 1231.
*
Keywords
Chemometrics; Computer-Based Learning; Mathematics / Symbolic Mathematics; Physical Chemistry; Quantum Chemistry; Upper-Division Undergraduate
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History
Created:
Last Updated:
5/29/2007
6/7/2007
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