Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 3 (2007), 112, 11 pages      arXiv:0710.0841      http://dx.doi.org/10.3842/SIGMA.2007.112
Contribution to the Proceedings of the Seventh International Conference Symmetry in Nonlinear Mathematical Physics

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

Alexandre M. Gavrilik and Anastasiya P. Rebesh
Bogolyubov Institute for Theoretical Physics, 14-b Metrologichna Str., 03680 Kyiv, Ukraine

Received October 09, 2007, in final form November 13, 2007; Published online November 22, 2007

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 E1 = E2 and E3 = E4. On the other hand, using one fixed quadratic relation, we obtain p-oscillators with other cases of two pairs of (pairwise) degenerate energy levels.

Key words: q,p-deformed oscillators; q-oscillators; energy levels degeneracy; energy function.

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