Non-Hermitian oscillator Hamiltonians and multiple Charlier 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.

15 pages

References in corpus (2)

• The nearest neighbor recurrence coefficients for multiple orthogonal polynomials
• Representations of the Schrödinger group and matrix orthogonal polynomials

Cited by in corpus (7)

• What is $\dots$ a multiple orthogonal polynomial?
• Multidimensional Toda Lattices: Continuous and Discrete Time
• An Algebraic Model for the Multiple Meixner Polynomials of the First Kind
• Multiple Meixner polynomials and non-Hermitian oscillator Hamiltonians
• On the $q$-Charlier Multiple Orthogonal Polynomials
• Asymptotics for the ratio and the zeros of multiple Charlier polynomials
• Multiple q-Kravchuk polynomials