Geodesic
Deformed Oscillators with Two Double (Pairwise) Degeneracies of Energy Levels
Symmetry, integrability and geometry: methods and applications, Tome 3 (2007) Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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.
Keywords: $q,\!p$-deformed oscillators; $q$-oscillators; energy levels degeneracy; energy function. 
@article{SIGMA_2007_3_a111,
     author = {Alexandre M. Gavrilik and Anastasiya P. Rebesh},
     title = {Deformed {Oscillators} with {Two} {Double} {(Pairwise)} {Degeneracies} of {Energy} {Levels}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2007},
     volume = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a111/}
}
TY  - JOUR
AU  - Alexandre M. Gavrilik
AU  - Anastasiya P. Rebesh
TI  - Deformed Oscillators with Two Double (Pairwise) Degeneracies of Energy Levels
JO  - Symmetry, integrability and geometry: methods and applications
PY  - 2007
VL  - 3
UR  - http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a111/
LA  - en
ID  - SIGMA_2007_3_a111
ER  - 
%0 Journal Article
%A Alexandre M. Gavrilik
%A Anastasiya P. Rebesh
%T Deformed Oscillators with Two Double (Pairwise) Degeneracies of Energy Levels
%J Symmetry, integrability and geometry: methods and applications
%D 2007
%V 3
%U http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a111/
%G en
%F SIGMA_2007_3_a111
Alexandre M. Gavrilik; Anastasiya P. Rebesh. Deformed Oscillators with Two Double (Pairwise) Degeneracies of Energy Levels. Symmetry, integrability and geometry: methods and applications, Tome 3 (2007). http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a111/

[1] Arik M., Coon D. D., “Hilbert spaces of analytic functions and generalized coherent states”, J. Math. Phys., 17 (1976), 524–527 | DOI | MR

[2] Biedenharn L. C., “The quantum group $SU_q(2)$ and a $q$-analogue of the boson operators”, J. Phys. A: Math. Gen., 22 (1989), L873–878 | DOI | MR

[3] Macfarlane A. J., “On $q$-analogues of the quantum harmonic oscillator and the quantum group $SU_q(2)$”, J. Phys. A: Math. Gen., 22 (1989), 4581–4585 | DOI | MR

[4] Odaka K., Kishi T., Kamefuchi S., “On quantization of simple harmonic oscillator”, J. Phys. A: Math. Gen., 24 (1991), L591–L596 | DOI | MR | Zbl

[5] Chaturvedi S., Srinivasan V., Jagannathan R., “Tamm–Dancoff deformation of bosonic oscillator algebras”, Modern Phys. Lett. A, 8 (1993), 3727–3734 | DOI | MR | Zbl

[6] Chakrabarti A., Jagannathan R., “A $q,\!p$-oscillator realization of two-parameter quantum algebras”, J. Phys. A: Math. Gen., 24 (1991), L711–L718 | DOI | Zbl

[7] 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 | DOI | MR | Zbl

[8] 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 | DOI | MR

[9] Meljanac S., Milekovic M., Pallua S., “Unified view of deformed single-mode oscillator algebras”, Phys. Lett. B, 328 (1994), 55–59 ; hep-th/9404039 | DOI | MR

[10] Landau L. D., Lifshitz E. M., Quantum mechanics (nonrelativistic theory), Fiz.-Mat. Lit., Moscow, 1963 (in Russian) | MR

[11] Kar S., Parwani R. R., “Can degenerate bounds states occur in one dimensional quantum mechanics?”, Europhys. Lett., 80:3 (2007), Art. 30004, 5 pp., ages ; arXiv:0706.1135 | DOI | MR

[12] 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 | DOI | MR | Zbl

[13] Gavrilik A. M., Rebesh A. P., Occurrence of pairwise energy level degeneracies in $q,\!p$-oscillator model, submitted

[14] 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 | DOI | MR | Zbl

[15] Lorek A., Wess J., “Dynamical symmetries in $q$-deformed quantum mechanics”, Z. Phys. C, 67 (1995), 671–680 ; q-alg/9502007 | DOI | MR

[16] Gavrilik A. M., “Combined analysis of two- and three-particle correlations in the $q,\!p$-Bose gas model”, SIGMA, 2 (2006), 074, 12 pp., ages ; hep-ph/0512357 | MR | Zbl

[17] 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

[18] 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 | DOI