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

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.