QUASI-EXACTLY SOLVABLE SYSTEMS AND ORTHOGONAL POLYNOMIALS

This paper shows that there is a correspondence between quasi-exactly solvable models in quantum mechanics and sets of orthogonal polynomial s {P-n}. The quantum-mechanical wave function is the generating functi on for the P-n(E), which are polynomials in the energy E. The conditio n of quasi-exact solvability is reflected in the vanishing of the norm of all polynomials whose index n exceeds a critical value J. The zero s of the critical polynomial P-J(E) are the quasi-exact energy eigenva lues of the system. (C) 1996 American Institute of Physics.