Orthogonal Polynomials of a discrete variable as expansion basis sets in quantum machanics.The hyperquantization algorithm.

In recent years, orthogonal polynomials of a discrete variable have been widely investigated both as tools of numerical analysis for the rapresentation of functions on grids and as the superposition coefficients which appear as matrix alements of the overlap between spherical and hyperspherical harmonics corresponding to alternative coordinate systems.This paper reviews our work concerning the extension of their use to quantum mechanical problems.By exploiting both their connection with coupling and recoupling coefficients of angular momentum theory and their asymptotic relationships(semiclassical limit)with spherical and hyperspherical harminics, a discretization procedure, the hyperquantization algorithm, has been developed and applied to the study of anisotropic interactions and of reactive scattering as a quanum mechanical n-body problem.