Deformed Oscillators with Two Double (Pairwise) Degeneracies of Energy Levels

TL;DR

This paper introduces a method to construct special q-oscillator models with two pairs of degenerate energy levels by using two-parameter deformed oscillators and specific relations between parameters.

Contribution

It presents a novel approach to generate q-oscillator models with multiple degeneracies through particular relations between deformation parameters p and q.

Findings

Constructed q-oscillator models with two pairs of degenerate energy levels.

Utilized quadratic relations p=f(q) to achieve degeneracies.

Provided different versions of degeneracy configurations.

Abstract

A scheme is proposed which allows to obtain special $q$-oscillator models whose characteristic feature consists in possessing two differing pairs of degenerate energy levels. The method uses the model of two-parameter deformed $q,p$-oscillators and proceeds via appropriately chosen particular relation between $p$ and $q$. Different versions of quadratic relations $p=f(q)$ are utilized for the case which implies two degenerate pairs $E_1=E_2$ and $E_3=E_4$. On the other hand, using one fixed quadratic relation, we obtain $p$-oscillators with other cases of two pairs of (pairwise) degenerate energy levels.