Two-dimensional quasi-exactly solvable models and classical orthogonal polynomials

Abstract

New types of two-dimensional quasi-exactly solvable models are found. They are obtained from one-dimensional finite-difference equations with the help of the generating function which is composed from a set of functions obeying simple recurrence equations. In particular, this set can consist of some kinds of classical orthogonal polynomials. It is shown that the models found are described in terms of SO(2,1) and Heisenberg-Weyl dynamical algebras.