标题： 从海森堡矩阵力学到EBK量子化：理论与初步应用 显示英文标题

标题： From Heisenberg matrix mechanics to EBK quantization: theory and first applications

摘要： 尽管经典多周期运动与海森堡矩阵力学之间具有开创性的联系，并且在与此相关的束缚态半经典（EBK）量子化问题上已经做了大量工作，我们仍然表明，这种关系中仍有一些以前未被利用的方面与量子-经典对应关系有关。 特别是，我们强调了一个量子变分原理，该原理暗示了不变环面的经典变分原理。 我们还揭示了对易关系与作用变量量子化的更为间接的联系。 借助几个具有一个或两个自由度的标准模型，我们展示了本文描述的海森堡矩阵力学方法如何以适度增加的努力来获得量子解，相比半经典计算而言。 我们还描述并应用了一种获取EBK结果的首阶量子修正的方法。 最后，我们提出了EBK量子化的一些新应用或修改应用。 显示英文摘要

摘要： Despite the seminal connection between classical multiply-periodic motion and Heisenberg matrix mechanics and the massive amount of work done on the associated problem of semiclassical (EBK) quantization of bound states, we show that there are, nevertheless, a number of previously unexploited aspects of this relationship that bear on the quantum-classical correspondence. In particular, we emphasize a quantum variational principle that implies the classical variational principle for invariant tori. We also expose the more indirect connection between commutation relations and quantization of action variables. With the help of several standard models with one or two degrees of freedom, we then illustrate how the methods of Heisenberg matrix mechanics described in this paper may be used to obtain quantum solutions with a modest increase in effort compared to semiclassical calculations. We also describe and apply a method for obtaining leading quantum corrections to EBK results. Finally, we suggest several new or modified applications of EBK quantization.