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  Home > JCE Print > Journal of Chemical Education > Issues > 2008  > March  >
Research: Science and Education
Advanced Chemistry Classroom and Laboratory
The Harmonic Oscillator with a Gaussian Perturbation: Evaluation of the Integrals and Example Applications
Boyd L. Earl
Department of Chemistry, University of Nevada, Las Vegas, Las Vegas, NV 89154-4003
Cover
March 2008
Vol. 85 No. 3
p. 453
Abstract
A general result for the integrals of the Gaussian function over the harmonic oscillator wavefunctions is derived using generating functions. Using this result, an example problem of a harmonic oscillator with various Gaussian perturbations is explored in order to compare the results of precise numerical solution, the variational method, and perturbation theory. This model problem will provide instructors of quantum chemistry with an additional example for instructional use. An additional example in which a potential of this form is used to model the ammonia vibrational spectrum is included in summary form.
Supplement
Mathematical details of the Ammonia Example; Mathcad files for the Numerov procedure, the variation method solution, and the perturbation theory solution
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Contents
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JCE2008p0453W.zip
JCE2008p0453W.doc (Microsoft Word)
More Information
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Citation
Earl, Boyd L. J. Chem. Educ. 2008, 85, 453.
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Keywords
Mathematics / Symbolic Mathematics; Physical Chemistry; Quantum Chemistry; Spectroscopy; Upper-Division Undergraduate
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History
Created:
Last Updated:
2/4/2008
2/11/2008
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