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The Chemical Educator

ISSN: 1430-4171 (electronic version)

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Abstract Volume 15 (2010) pp 243-246

The Quantum Mechanical Spherical Harmonic Oscillator: A Central Field Problem

Larry Eno

Department of Chemistry and Biomolecular Science, Clarkson University, Potsdam, NY 13699-5810,
Received March 4, 2008. Accepted May 15, 2009.

Published: 15 June 2010

Abstract. The quantum mechanical motion of a particle in a central field - here referred to as the central field problem - is prominently featured in the core physical chemistry curriculum. While analysis of the general problem is appropriately effected using spherical polar coordinates, many students find daunting the use of spherical polar coordinates in this context. With this in mind, it may be helpful to introduce analysis of the central field problem through a case which can be readily solved using Cartesian coordinates, specifically the spherical harmonic oscillator. A presentation is given of the spherical harmonic oscillator at the level of the core physical chemistry courses.

Key Words: In the Classroom; physical chemistry, quantum mechanics

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