类氢原子自旋轨道耦合经典分析中隐动量和隐能的影响
On the influence of hidden momentum and hidden energy in the classical analysis of spin-orbit coupling in hydrogenlike atoms
摘要：
在最近的一篇文章中，Kholmetskii，Missevitch和Yarmin [“关于类氢原子中自旋轨道耦合的经典分析”，Am. 78（4），2010年4月（428-432）]详细研究了半经典类氢原子中的自旋-轨道耦合，并确定需要考虑未包括在标准分析中的非库仑力。Kholmetskii等人，表明，实验测量的耦合继续获得时，新的力量被纳入分析。这就要求由于非库仑力引起的轨道半径的变化也要适当地考虑。在回应评论时，Kholmetskii等人，表明，实验测量的耦合继续获得时，所谓的“隐藏的动量”的力量也包括在内。然而，它已被假定，当隐藏的动量是非零的，相应的隐藏的能量也必须存在，这是不包括在总能量由Kholmetskii等人。隐藏的能量被假定必要获得相对论协变的描述。如果玻尔假设轨道角动量是以约化的普朗克常量的整数倍量子化的，那么包含隐藏能量会导致与实验确定的自旋-轨道耦合幅度不一致。经验结果可以在半经典图像中恢复，并使用Kholmetskii等人开发的一般方法，如果将波尔假设重新解释为适用于由隐藏动量和动能组成的轨道角动量。
英文摘要：
In a recent article, Kholmetskii, Missevitch and Yarmin ["On the classical analysis of spin-orbit coupling in hydrogenlike atoms," Am. J. Phys. 78(4), April 2010 (428-432)] examine in detail the spin-orbit coupling in the semiclassical hydrogenic atom, and identify a need to account for non-Coulomb forces not included in the standard analysis. Kholmetskii, et al., showed that the experimentally-measured coupling continues to be obtained when the new forces are incorporated in the analysis. This requires that the change in orbital radius due to non-Coulomb forces is also properly accounted for. In response to a comment, Kholmetskii, et al., showed that the experimentally-measured coupling continues to be obtained when so-called "hidden momentum" forces are also included. However it has been postulated that when hidden momentum is nonvanishing, a corresponding hidden energy must also be present, that was not included in the total energy by Kholmetskii, et al. Hidden energy is postulated necessary to obtaining a relativistically covariant description. Inclusion of hidden energy leads to disagreement with the experimentally-determined spin-orbit coupling magnitude if the Bohr postulate, that orbital angular momentum is quantized in whole multiples of the reduced Planck constant, is assumed to apply to kinetic momentum alone. The empirical result may be recovered in the semiclassical picture and using the general approach developed by Kholmetskii, et al., if the Bohr postulate is reinterpreted to apply to orbital angular momentum that consists of hidden as well as kinetic momentum.
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