Non-Hermitian oscillator Hamiltonians and multiple Charlier polynomials

2011/06/26 by Hiroshi Miki, Luc Vinet, Alexei Zhedanov · 14 citations
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic number #Computer science #Diagonalizable matrix #Discrete orthogonal polynomials #Eigenvalues and eigenvectors #Hermitian matrix #Interpretation (philosophy) #Mathematical analysis #Mathematics #Orthogonal polynomials #Physics #Pure mathematics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #Spectroscopy and Quantum Chemical Studies #Symmetric matrix #Tridiagonal matrix #math-ph #math.MP #msc:20C35 #msc:33C80 #msc:42C05 #msc:81R05 #msc:81R30

paper · pdf · doi:10.1016/j.physleta.2011.10.038

published in Physics Letters A 376(2), 65-69 (Elsevier BV) · 15 pages

arxiv created 2011/06/26 · openalex publication_date 2011/11/01 · arxiv updated 2015/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
• Representations of the Schrödinger group and matrix orthogonal polynomials
• Classical and Quantum Orthogonal Polynomials in One Variable

Cited by

• On the q-Charlier Multiple Orthogonal Polynomials