超可积势的代数处理
Algebraic treatment of super-integrable potentials
摘要：
将这样的$(2,1)$李代数应用于三类二维和三维Smorodinsky-Winternitz超可积势，并讨论了它们的路径积分.我们构造了$R^{2}.$中两个重要超可积势的格林函数。在$R^{3}$中的超可积势中，我们考虑了两个例子，一个是极大超可积的，另一个是极小超可积的。讨论是在各种坐标系中进行的。然后推导出束缚态和连续态的能谱和适当归一化的波函数。
英文摘要：
The so$(2,1)$ Lie algebra is applied to three classes of two- and three-dimensional Smorodinsky-Winternitz super-integrable potentials for which the path integral discussion has been recently presented in the literature. We have constructed the Green's functions for two important super-integrable potentials in $R^{2}.$ Among the super-integrable potentials in $R^{3}$, we have considered two examples, one is maximally super-integrable and another one minimally super-integrable. The discussion is made in various coordinate systems. The energy spectrum and the suitably normalized wave functions of bound and continuous states are then deduced.
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