Abstract
In the present paper on superintegrable potentials on spaces of constant 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 soluble cases the path-integral solutions explicitly in terms of the propagators and the spectral expansions in the wave functions. We find the analogs of the maximally and minimally superintegrable potentials of R 3 on 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 oscillator and the Kepler problem.
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