  To a crystallographic root system we associate a system of multivariate
orthogonal polynomials diagonalizing an integrable system of discrete pseudo
Laplacians on the Weyl chamber. We develop the time-dependent scattering theory
for these discrete pseudo Laplacians and determine the corresponding wave
operators and scattering operators in closed form. As an application, we
describe the scattering behavior of certain hyperbolic Ruijsenaars-Schneider
type lattice Calogero-Moser models associated with the Macdonald polynomials.
