The symmetric q-oscillator algebra: q-coherent states, q-Bargmann–Fock realization and continuous q-Hermite polynomials with 0 < q < 1

DOI10.1142/S0219887816500286zbMath1405.81048MaRDI QIDQ2802585

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Publication date: 26 April 2016

Published in: International Journal of Geometric Methods in Modern Physics (Search for Journal in Brave)

zbMATH Keywords

\(q\)-Hermite polynomials\(q\)-calculus\(q\)-oscillator algebras\(q\)-deformed coherent states

Mathematics Subject Classification ID

(q)-calculus and related topics (05A30) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Coherent states (81R30) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45)

Related Items (6)

Introduction of the numerical methods in quantum calculus with uncertainty ⋮ \(q\)-coherent states associated with the noncommutative complex plane \(\mathbb C_{q^2}\) for the Biedenharn-Macfarlane \(q\)-oscillator ⋮ Coherent states attached to the quantum disc algebra and their associated polynomials ⋮ Nonclassical properties of the Arik–Coon q−1-oscillator coherent states on the noncommutative complex plane ℂq ⋮ Arik–Coon q-oscillator cat states on the noncommutative complex plane ℂq−1 and their nonclassical properties ⋮ Nonclassicality of photon-added \(q\)-squeezed first excited states

Cites Work

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• P,Q-differentiation, P,Q-integration, and P,Q-hypergeometric functions related to quantum groups
• Generalized q-oscillators and their Hopf structures

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