Occurrence of pairwise energy level degeneracies in q,p-oscillator model

TL;DR

This paper explores how a two-parameter deformed q,p-oscillator exhibits accidental pairwise degeneracies in its energy levels, revealing specific conditions for such degeneracies and their general forms.

Contribution

It introduces conditions for energy level degeneracies in q,p-oscillators and discusses their general cases, expanding understanding of their spectral properties.

Findings

q,p-oscillators exhibit accidental two-fold degeneracies

Degeneracy conditions depend on deformation parameters q and p

General degeneracy forms are identified and discussed

Abstract

It is demonstrated that a two-parameter deformed oscillator with the deformation parameters q,p such that 0 < q,p \le 1 exhibits the property of "accidental" two-fold (pairwise) energy level degeneracy of the classes E_m=E_{m+1} and E_0=E_{m}. The most general case of degeneracy of q,p-oscillators of the form E_{m+k}=E_m (with k\ge 1 for m\ge 1 or k\ge 2 for m=0) is briefly discussed.