非常曲率空间上超可积势的路径积分方法：II。达布空间DIII和DIV
Path Integral Approach for Superintegrable Potentials on Spaces of Non-constant Curvature: II. Darboux Spaces DIII and DIV
摘要：
这是第二篇关于达布空间（非常曲率空间）上超可积系统的路径积分方法的论文。我们在空间$\DIII$和$\DIV$中分别分析了Kalnins等人首先给出的5个4个超可积势。我们能够计算大多数分离坐标系中的路径积分，从而得到格林函数、离散和连续波函数以及离散能谱的表达式。然而，在某些情况下，离散谱不能明确地陈述，因为它是由高阶多项式方程确定的。我们还表明，自由运动的达布空间的III型可以包含束缚态，提供适当的边界条件。我们的状态的能量谱和波函数，分别。
英文摘要：
This is the second paper on the path integral approach of superintegrable systems on Darboux spaces, spaces of non-constant curvature. We analyze in the spaces $\DIII$ and $\DIV$ five respectively four superintegrable potentials, which were first given by Kalnins et al. We are able to evaluate the path integral in most of the separating coordinate systems, leading to expressions for the Green functions, the discrete and continuous wave-functions, and the discrete energy-spectra. In some cases, however, the discrete spectrum cannot be stated explicitly, because it is determined by a higher order polynomial equation. We show that also the free motion in Darboux space of type III can contain bound states, provided the boundary conditions are appropriate. We state the energy spectrum and the wave-functions, respectively.
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