A superintegrable discrete harmonic oscillator based on bivariate Charlier polynomials

TL;DR

This paper introduces a new discrete model of the 2D isotropic harmonic oscillator using bivariate Charlier polynomials, demonstrating superintegrability with su(2) symmetry, expanding the class of such models.

Contribution

It presents a novel superintegrable discrete oscillator model based on bivariate Charlier polynomials, complementing existing models using other orthogonal polynomials.

Findings

Model exhibits superintegrability with su(2) symmetry

Extends discrete oscillator models to include bivariate Charlier polynomials

Adds to existing models based on Krawtchouk and Meixner polynomials

Abstract

A simple discrete model of the two dimensional isotropic harmonic oscillator is presented. It is superintegrable with su(2) as its symmetry algebra. It is constructed with the help of the algebraic properties of the bivariate Charlier polyno-mials. This adds to the other discrete superintegrable models of the oscillator based on Krawtchouk and Meixner orthogonal polynomials in several variables.