Superintegrability on the two-dimensional hyperboloid. II

This work is devoted to the investigation of the quantum mechanical systems on the two-dimensional hyperboloid which admits separation of variables in at least two coordinate systems. Here we consider two potentials introduce d in a paper of C. P. Boyer, E. G. Kalnins, and P. Winternitz [J. Math. Phy s. 24, 2022 (1983)], which have not yet been studied. We give an example of an interbasis expansion and work out the structure of the quadratic algebr a generated by the integrals of motion. (C) 1999 American Institute of Phys ics. [S0022-2488(99)00505-8].