PATH-INTEGRAL APPROACH FOR SUPERINTEGRABLE POTENTIALS ON THE 3-DIMENSIONAL HYPERBOLOID

In the present paper on superintegrable potentials on spaces of consta nt curvature we discuss the case of the three-dimensional hyperboloid. Whereas in many coordinate systems an explicit path-integral solution for the corresponding potential is not possible, we list in the solub le cases the path-integral solutions explicitly in terms of the propag ators and the spectral expansions in the wave functions. We find the a nalogs of the maximally and minimally superintegrable potentials of R- 3 the hyperboloid and many minimally superintegrable potentials which emerge from the subgroup chains corresponding to SO(3,1). Some special care is taken for the proper generalization of the harmonic oscillato r and the Kepler problem. (C) 1997 American Institute of Physics.