Gavrilik, Alexandre M.; Rebesh, Anastasiya P.

Deformed oscillators with two double (pairwise) degeneracies of energy levels

SIGMA, Symmetry Integrability Geom. Methods Appl. 3, Paper 112, 11 p., electronic only (2007)


Summary: 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.

Mathematics Subject Classification

81S05, 81R50


$q$, p$-deformed oscillators$, $q$-oscillators, energy levels degeneracy, energy function