Generalized \(q\)-Hermite polynomials

DOI10.1007/PL00005583zbMath0989.81004OpenAlexW2084493188MaRDI QIDQ5953692

Christian Berg, Andreas Ruffing

Publication date: 27 January 2002

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/pl00005583

zbMATH Keywords

orthogonal polynomialsdiscrete \(q\)-Hermite polynomials of type IIexponential latticesymmetric ground statesymmetrized \(q\)-Laguerre polynomials

Mathematics Subject Classification ID

Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) (81P10) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Linear difference operators (47B39) Applications of basic hypergeometric functions (33D90)

Related Items (12)

Difference ladder operators for a harmonic Schrödinger oscillator using unitary linear lattices ⋮ The discretized harmonic oscillator: Mathieu functions and a new class of generalized Hermite polynomials ⋮ Characterization of \(q\)-Dunkl Appell symmetric orthogonal \(q\)-polynomials ⋮ A class of symmetric \(q\)-orthogonal polynomials with four free parameters ⋮ Permanence and existence of positive periodic solution for a multi-species cooperation system with continuous time delays, feedback control, and periodic external source ⋮ Difference-differential operators for basic adaptive discretizations and their central function systems ⋮ On the complex zeros of some families of orthogonal polynomials ⋮ Spectral analysis of quantum Dirac systems ⋮ Quadraticeigenparameter-dependent quantum difference equations ⋮ Spectral analysis of \(q\)-difference equations with spectral singularities ⋮ The category of ladders ⋮ Analytic aspects ofq-delayed exponentials: minimal growth, negative zeros and basic ghost states

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