Factorizacion of the hypergeometric-type difference equation on the uniform lattice

TL;DR

This paper explores the factorization of hypergeometric-type difference equations on uniform lattices, constructing dynamical algebras and unifying various models of discrete harmonic oscillators.

Contribution

It introduces a method to factorize these difference equations and develop associated dynamical algebras, unifying multiple discrete oscillator models.

Findings

Constructed dynamical algebras for hypergeometric difference equations

Unified treatment of various discrete harmonic oscillator models

Demonstrated the approach with multiple examples

Abstract

We discuss factorization of the hypergeometric-type difference equations on the uniform lattices and show how one can construct a dynamical algebra, which corresponds to each of these equations. Some examples are exhibited, in particular, we show that several models of discrete harmonic oscillators, previously considered in a number of publications, can be treated in a unified form.