Creation and Annihilation Operators for Orthogonal Polynomials of Continuous and Discrete Variables

TL;DR

This paper develops general creation and annihilation operators for orthogonal polynomials of hypergeometric type, analyzing their algebraic properties for various discrete and continuous cases, enhancing understanding of their mathematical structure.

Contribution

It introduces a unified framework for raising and lowering operators applicable to multiple classes of orthogonal polynomials, expanding their algebraic understanding.

Findings

Operators constructed for Kravchuk, Hermite, Meixner, and Laguerre polynomials.

Algebraic properties of these operators analyzed.

Framework applicable to both discrete and continuous variables.

Abstract

We develop general expressions for the raising and lowering operators that belong to the orthogonal polynomials of hypergeometric type with discrete and continuous variable. We construct the creation and annihilation operators that correspond to the normalized polynomials and study their algebraic properties in the case of the Kravchuk/Hermite Meixner/Laguerre polynomials.