Plethora of q-oscillators possessing pairwise energy level degeneracy

TL;DR

This paper introduces new classes of q-deformed oscillators with pairwise energy level degeneracies, expanding the understanding of their spectral properties and including known models as special cases.

Contribution

It develops diverse classes of q,p-deformed oscillators exhibiting accidental degeneracies, unifying and extending previous models including the Tamm-Dancoff oscillator.

Findings

Multiple classes of q-deformed oscillators with energy degeneracies

Degeneracy conditions depend on deformation parameters q(m) and q(k)

Includes the Tamm-Dancoff oscillator as a special case

Abstract

Using the q,p-deformed oscillators as basic generating system, we obtain diverse classes (which form distinct sectors of functional continua) of novel versions of q-deformed oscillators, all of which share the property of "accidental" degeneracy within a fixed pair of energy levels E_{m} = E_{m+1}, m\ge 1, occurring at the real deformation parameter fixed by an appropriate value q(m) that depends on m and on particular model. Likewise, the degeneracy E_{0} = E_{k} (where k\ge 2) takes place, for properly fixed q=q(k), in most of those models. The formerly studied model of q-oscillator known as the Tamm-Dancoff cutoff deformed oscillator is contained in the continua as isolated special case.