Koenigs非常曲率空间上量子运动的路径积分方法
Path Integral Approach for Quantum Motion on Spaces of Non-constant Curvature According to Koenigs
摘要：
在这篇文章中，我讨论了量子运动的路径积分方法在二维空间根据柯尼希斯，简称"柯尼希斯空间“。它们的构造很简单：从二维平坦空间中取一个哈密顿量，并将其除以一个二维超可积势。这些超可积势是各向同性奇异振子、霍尔特势和库仑势。在所有情况下，生成了一个具有非常曲率的非平凡空间。我们可以研究自由运动和附加超可积势的运动。对于可能的束缚态解，我们发现在所有三种情况下，能量E都是一个八阶方程。达布空间的特殊情况很容易通过选择相应的参数恢复。
英文摘要：
In this contribution I discuss a path integral approach for the quantum motion on two-dimensional spaces according to Koenigs, for short ``Koenigs-Spaces''. Their construction is simple: One takes a Hamiltonian from two-dimensional flat space and divides it by a two-dimensional superintegrable potential. These superintegrable potentials are the isotropic singular oscillator, the Holt-potential, and the Coulomb potential. In all cases a non-trivial space of non-constant curvature is generated. We can study free motion and the motion with an additional superintegrable potential. For possible bound-state solutions we find in all three cases an equation of eighth order in the energy E. The special cases of the Darboux spaces are easily recovered by choosing the parameters accordingly.
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