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arXiv quant-ph/0112174quant-ph
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球对称系统在Aharonov-Bohm磁通量作用下的半经典量子化

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

W. F. Kao, P. G. Luan, D. H. Lin

摘要:

本文导出了具有球对称势$V(r) \sim r^ν$ $(-2<ν<\infty)$和Aharonov-Bohm磁通量的系统的半经典量子化定则。数值结果与已知的结果相比,模型与$ν= -1,0,2,\infty$。结果表明,我们的方法提供的结果与以前的结果非常一致。即使是在大主量子数极限$n \gg 1$下导出的半经典量子化定则,也可以很好地近似所有的主量子数.本文还讨论了能谱图的功率参数$ν$依赖性。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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