On the Stark effect of the plane rotator
作者:
George L. Johnston,
Garrison Sposito,
期刊:
American Journal of Physics
(AIP Available online 1976)
卷期:
Volume 44,
issue 8
页码: 723-728
ISSN:0002-9505
年代: 1976
DOI:10.1119/1.10119
出版商: American Association of Physics Teachers
数据来源: AIP
摘要:
The Stark effect of the plane rotator is a pedagogically appealing problem for undergraduate courses on quantum mechanics and, accordingly, has appeared in a number of textbooks as an application of bound‐state perturbation theory. Despite this fact and the apparent simplicity of the problem, all of the published accounts of it are erroneous in that they employ nondegenerate perturbation theory and present incorrect expressions for the perturbed eigenvalues and eigenstates. In this paper the problem is given a new treatment, based upon a simple analysis of symmetry features and a careful application of degenerate perturbation theory. The major shortcomings of previous discussions are pointed out and correct expressions are derived, to second order, for the perturbed state vectors and energy levels. The lifting of the twofold degeneracy of themth unperturbed excitation energy in the 2mth order of perturbation theory is demonstrated. Finally, a comparison of the correct perturbation‐theoretic results with the exact solution of the problem shows the two to be in identical correspondence.
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