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  Home > JCE Print > Journal of Chemical Education > Issues > 2007  > July  >
Information • Textbooks • Media • Resources
JCE SymMath: Symbolic Mathematics in Chemistry
Exploring the Harmonic Oscillator Wave Functions
Theresa Julia Zielinski
Department of Chemistry, Medical Technology, and Physics, Monmouth University, West Long Branch, NJ 07764
Cover
July 2007
Vol. 84 No. 7
p. 1232
Abstract
The goal of this document is to have students explore the solutions to the quantum mechanical harmonic oscillator Schrödinger equation. Students do this by examining the exponential component, generating the various Hermite polynomials, and then creating the final HO wave functions as a product of a normalization factor, the exponential component, and a Hermite polynomial. Students also prepare plots of several harmonic oscillator wave functions and probability densities. The plots created with Mathcad provide an effective way for students to draw their own figures and master understanding of the concepts involved. Finally, students can examine the plots at both high and low quantum numbers and correlate their observations with classical harmonic oscillator predictions of maximum and minimum kinetic energy and maximum probability of the extension of the oscillator.

Plots of 1st, 2nd, and 4th harmonic oscillator wave functions drawn with Mathcad. Students can generate many such plots and explore their properties.
Supplement
Fully interactive computer algebra files are available in the JCE SymMath collection of the JCE Digital Library Only@JCE Online.
More Information
*
Citation
Zielinski, Theresa Julia. J. Chem. Educ. 2007, 84, 1232.
*
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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