Polynomials of a discrete variable, dynamical, symmetries and quantum mechanics

In the case of exactly solvable problems, the dynamical symmetries give a group theoretical setting for the Lanczos method. They will be used to obtain recurrence relations for classical orthogonal polynomials of a discrete variable. Specifically, the one-dimensional harmonic oscillator and the radial part of the Schrodinger equation for the three-dimensional harmonic oscillator and the hydrogen atom are shown to provide an algebraic interpretation of the Charlier and Meixner polynomials respectively. As a by product, realizations of the oscillator and su(1,1) algebras in terms of finite difference operators can be constructed. The connection with coherent states is also mentioned. (Author) 4 refs