Semiclassical quantization for the spherically symmetric systems under an Aharonov-Bohm magnetic flux

The semiclassical quantization rule is derived for a system with a spherically symmetric potential V(r)∼rν(-2<ν<∞) and an Aharonov-Bohm magnetic flux. Numerical results are presented and compared with known results for models with ν=-1,0,2,∞. 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 numbers, including the large principle quantum number n>>1. The rule is even derived in the large principal quantum number limit n>>1. We also discuss the power parameter ν dependence of the energy spectra pattern in this paper