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SIGMA 3 (2007), 112, 11 pages arXiv:0710.0841
https://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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References
- Arik M., Coon D.D., Hilbert spaces of analytic functions and
generalized coherent states, J. Math. Phys. 17 (1976),
524-527.
- Biedenharn L.C., The quantum group SUq(2) and a
q-analogue of the boson operators, J. Phys. A: Math. Gen.
22 (1989), L873-878.
- Macfarlane A.J., On q-analogues of the quantum harmonic oscillator
and the quantum group SUq(2),
J. Phys. A: Math. Gen. 22 (1989), 4581-4585.
- Odaka K., Kishi T., Kamefuchi S.,
On quantization of simple harmonic oscillator, J. Phys. A: Math.
Gen. 24 (1991), L591-L596.
- Chaturvedi S., Srinivasan V., Jagannathan R.,
Tamm-Dancoff deformation of bosonic oscillator algebras, Modern
Phys. Lett. A 8 (1993), 3727-3734.
- Chakrabarti A., Jagannathan R.,
A q,p-oscillator realization of two-parameter quantum algebras,
J. Phys. A: Math. Gen. 24 (1991), L711-L718.
- Mizrahi S.S., Camargo Lima J.P., Dodonov V.V.,
Energy spectrum, potential and inertia functions of a generalized
f-oscillator, J. Phys. A: Math. Gen. 37 (2004),
3707-3724.
- Man'ko V.I., Marmo G., Sudarshan E.C.G., Zaccaria F., f-oscillators
and nonlinear coherent states, Phys. Scripta 55
(1997), 528-541, quant-ph/9612006.
- Meljanac S., Milekovic M., Pallua S.,
Unified view of deformed single-mode oscillator algebras, Phys.
Lett. B 328 (1994), 55-59, hep-th/9404039.
- Landau L.D., Lifshitz E.M., Quantum mechanics (nonrelativistic theory),
Fiz.-Mat. Lit., Moscow, 1963 (in Russian).
- Kar S., Parwani R.R., Can degenerate bounds states
occur in one dimensional quantum mechanics?, Europhys.
Lett. 80 (2007), no. 3, 30004, 5 pages, arXiv:0706.1135.
- Gavrilik A.M., Rebesh A.P.,
A q-oscillator with "accidental" degeneracy of energy levels,
Modern Phys. Lett. A 22 (2007), 949-960, quant-ph/0612122.
- Gavrilik A.M., Rebesh A.P.,
Occurrence of pairwise energy level degeneracies in
q,p-oscillator model, submitted.
- Quesne C., Tkachuk V.M.,
Deformed algebras, position-dependent effective masses and curved
spaces: an exactly solvable Coulomb problem, J. Phys. A: Math. Gen.
37 (2004), 4267-4281, math-ph/0403047.
- Lorek A., Wess J.,
Dynamical symmetries in q-deformed quantum mechanics, Z.
Phys. C 67 (1995), 671-680, q-alg/9502007.
- Gavrilik A.M.,
Combined analysis of two- and three-particle correlations in the
q,p-Bose gas model, SIGMA 2 (2006), 074, 12 pages, hep-ph/0512357.
- Anchishkin D.V., Gavrilik A.M., Iorgov N.Z.,
Two-particle correlations from the q-boson viewpoint, Eur. J.
Phys. C. 7 (2000), 229-238, nucl-th/9906034.
- Anchishkin D.V., Gavrilik A.M., Iorgov N.Z.,
q-boson approach to multiparticle correlations, Modern Phys.
Lett. A 15 (2000), 1637-1646, hep-ph/0010019.
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