Generalized Lame functions. II. Hyperbolic and trigonometric specializations

In Part I [J. Math. Phys. 40, 1595 (1999)] we studied eigenfunctions of the quantum dynamics that defines the two-particle relativistic Calogero-Moser system with elliptic interaction. In the present paper we consider the sam e system with hyperbolic and trigonometric interactions. In these special r egimes the eigenfunctions are shown to admit an elementary representation t hat is far more explicit than the "zero representation'' of Part I. In part icular, the new representation can be exploited to prove that the hyperboli c eigenfunctions can be chosen to be symmetric under interchanging position and momentum variables (self-duality). In the trigonometric case duality p roperties are derived, too, and several orthogonality and completeness resu lts are obtained. (C) 1999 American Institute of Physics. [S0022-2488(99)02 502-5].