Perturbation Theory for a Particle in a Box

TCE

The Chemical Educator

ISSN: 1430-4171 (electronic version)

Table of Contents

Abstract Volume 10 Issue 3 (2005) pp 169-175
DOI 10.1333/s00897050896a

Perturbation Theory for a Particle in a Box

Henry E. Montgomery, Jr.* and William P. Crummett

Centre College, 600 West Walnut Street, Danville, KY 40422, mntgmry@centre.edu
Received November 30, 2004. Accepted February 28, 2005.

Published online: 21 March 2005

Abstract. Rayleigh–Schrödinger perturbation theory is used to find energy and wavefunction corrections for a particle confined in a box with infinite walls. The resulting perturbation equations have simple, analytic solutions. The procedure for normalization of the wavefunction corrections is demonstrated, and the perturbation energies and normalized wavefunctions are shown to approach the exact values. The method is applied to both the ground state and first excited state and can become a valuable component of a student’s introduction to perturbation analysis.

Key Words: In the Classroom; physical chemistry; quantum chemistry; perturbation theory

(*) Corresponding author. (E-mail: mntgmry@centre.edu)

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