2012
DOI: 10.15407/ujpe57.4.396
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Oscillators in the Framework of Unified (q, α, β, γ, ν)-Deformation and Their Oscillator Algebras

Abstract: The aim of this paper is to review our results on the description of multiparameter deformed oscillators and their oscillator algebras. We define generalized (q; α, β, γ, ν)-deformed oscillator algebras and study their irreducible representations. The Arik–Coon oscillator with the main relation aa+ – qa+a = 1, where q >1, is embedded in this framework. We have found the connection of this oscillator with the Askey q–1-Hermite polynomials. We construct a family of generalized coherent states associated with … Show more

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“…A generalization of the traditional scheme for the deformed algebras to the multiparametric case has been done in [14][15][16]. In this approach, only the structure functions are changed, but a part of the defining relations was kept invariable.…”
Section: Introductionmentioning
confidence: 99%
“…A generalization of the traditional scheme for the deformed algebras to the multiparametric case has been done in [14][15][16]. In this approach, only the structure functions are changed, but a part of the defining relations was kept invariable.…”
Section: Introductionmentioning
confidence: 99%