Unified $(p,q;\alpha ,\beta ,\nu ;\gamma )-$deformed oscillator algebra: irreducible representations and induced deformed harmonic oscillator

Abstract

A new deformed canonical commutation relation, generalizing various known deformations, is defined together with its structure function of deformation. Then, the related irreducible representations are characterized and classified. Finally, the discrete spectrum of the corresponding deformed harmonic oscillator Hamiltonian is investigated and discussed.

References in corpus (2)

• New q-deformed coherent states with an explicitly known resolution of unity
• Unified $(q;\alpha ,\beta ,\gamma ;\nu )$-deformation of one-parametric q-deformed oscillator algebras

Cited by in corpus (2)

• On realizations of polynomial algebras with three generators via deformed oscillator algebras
• Generalized q-deformed Tamm-Dancoff oscillator algebra and associated coherent states