Some Orthogonal Polynomials Arising from Coherent States

TL;DR

This paper investigates orthogonal polynomials linked to specific coherent states in quantum optics, revealing both known and new classes with several established properties.

Contribution

It introduces a general class of new orthogonal polynomials associated with nonlinear coherent states and analyzes their qualitative properties.

Findings

Identification of known orthogonal polynomials within the framework

Discovery of new orthogonal polynomials related to coherent states

Establishment of qualitative properties for these polynomials

Abstract

We explore in this paper some orthogonal polynomials which are naturally associated to certain families of coherent states, often referred to as nonlinear coherent states in the quantum optics literature. Some examples turn out to be known orthogonal polynomials but in many cases we encounter a general class of new orthogonal polynomials for which we establish several qualitative results.