C. Grosche et al., PATH-INTEGRAL APPROACH FOR SUPERINTEGRABLE POTENTIALS ON THE 3-DIMENSIONAL HYPERBOLOID, Physics of particles and nuclei, 28(5), 1997, pp. 486-519
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.