Systems of orthogonal polynomials defined by hypergeometric type equations with application to quantum mechanics

Abstract

A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated special functions and the corresponding raising/lowering operators. The considered equations are directly related to some Schrodinger type equations (Poschl-Teller, Scarf, Morse, etc), and the defined special functions are related to the corresponding bound-state eigenfunctions.