Unified $(q;\alpha ,\beta ,\gamma ;\nu )$-deformation of one-parametric q-deformed oscillator algebras

Abstract

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.

References in corpus (4)

• Explicit Solution to the N-Body Calogero Problem
• Unified View of Deformed Single - Mode Oscillator Algebras
• Quantum algebras in phenomenological description of particle properties
• Noncommutativity as a Possible Origin of the Ultrahigh Energy Cosmic Ray and the TeV-photon Paradoxes

Cited by in corpus (4)

• Calculating statistical distributions from operator relations: the statistical distributions of various intermediate statistics
• On realizations of polynomial algebras with three generators via deformed oscillator algebras
• Unified $(p,q;\alpha ,\beta ,\nu ;\gamma )-$deformed oscillator algebra: irreducible representations and induced deformed harmonic oscillator
• On the dimensions of oscillator-like algebras induced by orthogonal polynomials: non-symmetric case