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Semiclassical Quantization for the Spherically Symmetric Systems under an Aharonov-Bohm magnetic flux

W. F. Kao·P. G. Luan·D. H. Lin
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Abstract

The semiclassical quantization rule is derived for a system with a spherically symmetric potential $V(r) \sim r^ν$ $(-2<ν<\infty)$ and an Aharonov-Bohm magnetic flux. Numerical results are presented and compared with known results for models with $ν= -1,0,2,\infty$. It is shown that the results provided by our method are in good agreement with previous results. One expects that the semiclassical quantization rule shown in this paper will provide a good approximation for all principle quantum number even the rule is derived in the large principal quantum number limit $n \gg 1$. We also discuss the power parameter $ν$ dependence of the energy spectra pattern in this paper.

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W. F. Kao, P. G. Luan, D. H. Lin. 2002-02-03. Semiclassical Quantization for the Spherically Symmetric Systems under an Aharonov-Bohm magnetic flux. https://doi.org/10.1103/physreva.65.052108

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