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

TL;DR

This paper introduces a new generalized deformed oscillator algebra, characterizes its irreducible representations, and analyzes the spectrum of the associated deformed harmonic oscillator Hamiltonian.

Contribution

It proposes a unified $(p,q;\alpha,eta, u;\gamma)$-deformed algebra, providing a comprehensive framework for its representations and spectral properties.

Findings

Classification of irreducible representations

Analysis of the deformed harmonic oscillator spectrum

Generalization of known deformation models

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.