Non-Hermitian oscillator Hamiltonians and multiple Charlier polynomials

TL;DR

This paper introduces a set of non-Hermitian oscillator Hamiltonians in multiple dimensions, demonstrating their real spectra and expressing eigenstates via multiple Charlier polynomials, thus providing an algebraic understanding of these polynomials.

Contribution

It presents a novel class of non-Hermitian Hamiltonians with real spectra and links their eigenstates to multiple Charlier polynomials, offering new algebraic insights.

Findings

Hamiltonians are simultaneously diagonalizable with real spectra.

Eigenstates are expressed in terms of multiple Charlier polynomials.

The model provides an algebraic interpretation of these polynomials.

Abstract

A set of r non-Hermitian oscillator Hamiltonians in r dimensions is shown to be simultaneously diagonalizable. Their spectra is real and the common eigenstates are expressed in terms of multiple Charlier polynomials. An algebraic interpretation of these polynomials is thus achieved and the model is used to derive some of their properties.