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

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

2001-12-29

arxiv.org/abs/quant-ph/0112174v2

Physics

Quantum Physics

13 pages, 4 figures, some typos corrected

Scientific paper

10.1103/PhysRevA.65.052108

The semiclassical quantization rule is derived for a system with a spherically symmetric potential $V(r) \sim r^{\nu}$ $(-2<\nu <\infty)$ and an Aharonov-Bohm magnetic flux. Numerical results are presented and compared with known results for models with $\nu = -1,0,2,\infty$. 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 $\nu $ dependence of the energy spectra pattern in this paper.

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