PATH-INTEGRAL DISCUSSION FOR SMORODINSKY-WINTERNITZ POTENTIALS .1. 2-DIMENSIONAL AND 3-DIMENSIONAL EUCLIDEAN-SPACE

Path integral formulations for the Smorodinsky-Winternitz potentials i n two- and three-dimensional Euclidean space are presented. We mention all coordinate systems which separate the Smorodinsky-Winternitz pote ntials and state the corresponding path integral formulations. Whereas in many coordinate systems an explicit path integral formulation is n ot possible, we list in all soluble cases the path integral evaluation s explicitly in terms of the propagators and the spectral expansions i nto the wave-functions.