Geodesic
Integrable model of a two-dimensional singular spherical oscillator in
Teoretičeskaâ i matematičeskaâ fizika, Tome 156 (2008) no. 1, pp. 131-137 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We propose an analogue of a two-dimensional singular oscillator (Smorodinsky–Winternitz oscillator) on a sphere, which is exactly solvable in the classical sense both without and with a constant magnetic field. We find the explicit classical solutions.
Keywords: singular oscillator, magnetic field, integrable model. 
@article{TMF_2008_156_1_a6,
     author = {K. S. Aramyan},
     title = {Integrable model of a~two-dimensional singular spherical oscillator in},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {131--137},
     year = {2008},
     volume = {156},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2008_156_1_a6/}
}
TY  - JOUR
AU  - K. S. Aramyan
TI  - Integrable model of a two-dimensional singular spherical oscillator in
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2008
SP  - 131
EP  - 137
VL  - 156
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2008_156_1_a6/
LA  - ru
ID  - TMF_2008_156_1_a6
ER  - 
%0 Journal Article
%A K. S. Aramyan
%T Integrable model of a two-dimensional singular spherical oscillator in
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2008
%P 131-137
%V 156
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2008_156_1_a6/
%G ru
%F TMF_2008_156_1_a6
K. S. Aramyan. Integrable model of a two-dimensional singular spherical oscillator in. Teoretičeskaâ i matematičeskaâ fizika, Tome 156 (2008) no. 1, pp. 131-137. http://geodesic.mathdoc.fr/item/TMF_2008_156_1_a6/

[1] A. M. Perelomov, Integriruemye sistemy klassicheskoi mekhaniki i algebry Li, Nauka, M., 1990 | MR | Zbl

[2] V. I. Arnold, Matematicheskie metody klassicheskoi mekhaniki, Nauka, M., 1989 | MR | MR | Zbl

[3] P. W. Higgs, J. Phys. A, 12:3 (1979), 309–323 | DOI | MR | Zbl

[4] E. Schrödinger, Proc. Roy. Irish Soc., 46 (1940), 9–16 ; 46 (1941), 183–206 ; 47 (1941), 53–54 | MR | Zbl | MR | Zbl | MR | Zbl

[5] S. Bellucci, A. Nersessian, Phys. Rev. D, 67:6 (2003), 5013 | DOI

[6] S. Bellucci, A. Nersessian, A. Yeranyan, Phys. Rev. D, 70:8 (2004), 5013 | DOI | MR

[7] S. Bellucci, A. Nersessian, A. Yeranyan, Phys. Rev. D, 70:4 (2004), 5006 | DOI | MR

[8] M. A. Alexanyan, K. S. Aramyan, J. Contemp. Phys., 42:2 (2007), 49–54 | DOI

[9] A. Nersessian, A. Yeranyan, J. Phys. A, 37:7 (2004), 2791–2801 | DOI | MR | Zbl

[10] L. Mardoyan, A. Nersessian, Phys. Rev. B, 72:23 (2005), 3303 | DOI

[11] S. Bellucci, L. Mardoyan, A. Nersessian, Phys. Lett. B, 636:2 (2006), 137–141 | DOI | MR | Zbl

[12] L. Mardoyan, A. Nersessian, A. Yeranyan, Phys. Lett. A, 366:1–2 (2007), 30–35 | DOI

[13] R. B. Laughlin, Phys. Rev. Lett., 50:18 (1983), 1395–1398 | DOI

[14] S. C. Zhang, J. P. Hu, Science, 294:5543 (2001), 823–828 | DOI | MR

[15] P. Vinternitts, Ya. A. Smorodinskii, M. Uglirzh, I. Frish, YaF, 4 (1967), 625–635 ; J. Fris, V. Mandrasov, Ya. A. Smorodinsky, M. Uhlir, P. Winternitz, Phys. Lett., 16:3 (1965), 354–356 | MR | DOI | MR

[16] L. D. Landau, E. M. Lifshits, Mekhanika, Nauka, M., 1973 | MR | MR | Zbl

[17] G. B. Dvait, Tablitsy integralov i drugie matematicheskie formuly, Nauka, M., 1983 | MR | Zbl