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].