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Journal of Chemical Education

The particle in the one-dimensional champagne bottle revisited

Eduardo A. Castro, Francisco Marcelo Fernández

Published May 1, 1983• 0 citations
Publisher

Abstract

While the perturbation theory of the particle in a box is a good illustration of that theory, a serious difficulty arises when one tries to plot the perturbed ground state wavefunction to show those points explicitly.
DOI
10.1021/ed060p378

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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.