Unified $(q;α,β,γ;ν)$-deformation of one-parametric q-deformed oscillator algebras

Details Unified $(q;α,β,γ;ν)$-deformation of one-parametric q-deformed oscillator algebras Unified $(q;α,β,γ;ν)$-deformation of one-parametric q-deformed oscillator algebras

2008-06-03

arxiv.org/abs/0806.0613v1

Physics

Mathematical Physics

Scientific paper

10.1088/1751-8113/42/6/065201

We define a generalized $(q;\alpha,\beta,\gamma;\nu)$-deformed oscillator algebra and study the number of its characteristics. We describe the structure function of deformation, analyze the classification of irreducible representations and discuss the asymptotic spectrum behaviour of the Hamiltonian. For a special choice of the deformation parameters we construct the deformed oscillator with discrete spectrum of its "quantized coordinate" operator. We establish its connection with the (generalized) discrete Hermite I polynomials.

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