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arXiv · 1807.10067

Exactness of Bohr-Sommerfeld quantisation for two non-central potentials

David T. S. Perkins·Robert A. Smith
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Abstract

In this paper we demonstrate the integrability of the Hamilton-Jacobi equation for two non-central potentials in spherical polar coordinates, and present complete solutions for the classically bound orbits. We then show that the semiclassical method of Bohr-Sommerfeld quantisation exactly reproduces the bound state spectra of the corresponding quantum mechanical Schr\"odinger equations. One of these potentials has previously been analysed in parabolic coordinates; the results for the other are, to the authors' best knowledge, original.

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David T. S. Perkins, Robert A. Smith. 2018-07-26. Exactness of Bohr-Sommerfeld quantisation for two non-central potentials. https://doi.org/10.1088/1751-8121/aae4f2

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