  Shape invariance is an important ingredient of many exactly solvable quantum
mechanics. Several examples of shape invariant ``discrete quantum mechanical
systems" are introduced and discussed in some detail. They arise in the problem
of describing the equilibrium positions of Ruijsenaars-Schneider type systems,
which are "discrete" counterparts of Calogero and Sutherland systems, the
celebrated exactly solvable multi-particle dynamics. Deformed Hermite and
Laguerre polynomials are the typical examples of the eigenfunctions of the
above shape invariant discrete quantum mechanical systems.
