Generalized q-deformed oscillators, q-Hermite polynomials, generalized coherent states

2006/07/20 by Igor Burban, Burban, I. M.
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical functions and polynomials #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics

paper · pdf · doi:10.48550/arxiv.math-ph/0607045

openalex publication_date 2006/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of this paper is to study generalized q-analogs of the well-known q-deformed harmonic oscillators and to connect them with q-Hermite polynomials. We give a construction of the appropriate oscillator-like algebras and show that corresponding Hermite polynomials are generalization of the discrete q-Hermite I and the discrete q-Hermite II polynomials. We also construct generalized coherent states of Barut-Girardello type for oscillator-like systems connected with these polynomials.

Citations

• The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
• Generalized coherent states for q-oscillator connected with q-Hermite polynomials

Related

• Generalized coherent states for q-oscillator connected with q-Hermite polynomials
• Generalized discrete q-Hermite II polynomials and q-deformed oscillator
• Generalized Coherent States for q-oscillator connected with discrete q-Hermite polynomials
• Generalized deformed oscillators in framework of unified (q;α,β,γ;ν)-deformation and their oscillator algebras
• New q-Hermite polynomials: characterization, operator algebra and associated coherent states