Bender–Dunne Orthogonal Polynomials General Theory

Abstract

A general theory of Bender–Dunne orthogonal polynomials is proposed. It is shown that these polynomials can easily be constructed for any explicitly tridiagonalizable Hamiltonians and are, in fact, the orthogonal polynomials in a discrete variable which takes its values in the set of energy levels of the corresponding quantum model. The weight functions for Bender–Dunne polynomials are explicitly constructed.