量子Hamilton-Jacobi形式与束缚态谱
Quantum Hamilton-Jacobi formalism and the bound state spectra
摘要：
在经典力学中，周期系统的频率可以很容易地通过作用变量得到，而不需要完全求解运动方程。在量子哈密顿-雅可比形式中出现的等效量子作用量可以类似地提供束缚态问题的能量本征值，而不必显式地求解相应的薛定谔方程。这种优雅和有用的方法阐明了在这里的背景下，一些已知的和不那么众所周知的可解的潜力。它还示出，如何这种方法提供了一种理解，为什么近似的量化方案，如普通和超对称WKB，可以给某些潜在的确切答案。
英文摘要：
It is well known in classical mechanics that, the frequencies of a periodic system can be obtained rather easily through the action variable, without completely solving the equation of motion. The equivalent quantum action variable appearing in the quantum Hamilton-Jacobi formalism, can, analogously provide the energy eigenvalues of a bound state problem, without having to solve the corresponding Schrödinger equation explicitly. This elegant and useful method is elucidated here in the context of some known and not so well known solvable potentials. It is also shown, how this method provides an understanding, as to why approximate quantization schemes such as ordinary and supersymmetric WKB, can give exact answers for certain potentials.
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