Geodesic
Some quantum mechanical problems in Lobachevsky space
Teoretičeskaâ i matematičeskaâ fizika, Tome 109 (1996) no. 3, pp. 395-405 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

For potentials, being the solutions of Bertrand's problem in Lobachevsky space, quantum mechanical problems are considered. The self-adjointness of the corresponding Schrödinger operators is proved. Energy levels are calculated both from Schrödinger equation and by the Bohr–Sommerfeld method. The effect of quantum binding of classical infinite states is discovered. It is shown that the semiclassical limit is equivalent in some sense to the Euclidean one. 
@article{TMF_1996_109_3_a6,
     author = {A. V. Shchepetilov},
     title = {Some quantum mechanical problems in {Lobachevsky} space},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {395--405},
     year = {1996},
     volume = {109},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1996_109_3_a6/}
}
TY  - JOUR
AU  - A. V. Shchepetilov
TI  - Some quantum mechanical problems in Lobachevsky space
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1996
SP  - 395
EP  - 405
VL  - 109
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_1996_109_3_a6/
LA  - ru
ID  - TMF_1996_109_3_a6
ER  - 
%0 Journal Article
%A A. V. Shchepetilov
%T Some quantum mechanical problems in Lobachevsky space
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1996
%P 395-405
%V 109
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1996_109_3_a6/
%G ru
%F TMF_1996_109_3_a6
A. V. Shchepetilov. Some quantum mechanical problems in Lobachevsky space. Teoretičeskaâ i matematičeskaâ fizika, Tome 109 (1996) no. 3, pp. 395-405. http://geodesic.mathdoc.fr/item/TMF_1996_109_3_a6/

[1] P. E. Appel, Teoreticheskaya mekhanika, IL, M., 1960

[2] J. J. Slawianowski, Bull. Acad. pol. sci. Sér. sci. phys. et astron., 28:2 (1980), 99–108 | MR | Zbl

[3] V. V. Kozlov, Vest. MGU. Ser. 1, Matem. mekhan., 1994, no. 2, 28–35 | Zbl

[4] J. J. Slawianowski, J. Slominski, Bull. Acad. pol. sci. Sér. sci. phys. et astron., 28:2 (1980), 83–94 | MR | Zbl

[5] V. V. Kozlov, A. O. Harin, Celest. Mech. and Dynam. Astron., 54 (1992), 393–399 | DOI | MR | Zbl

[6] M. M. Postnikov, Lineinaya algebra, Nauka, M., 1986 | MR | Zbl

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

[8] V. V. Belov, E. M. Vorobev, Sbornik zadach po dopolnitelnym glavam matematicheskoi fiziki, Vyssh. shkola, M., 1978 | MR

[9] B. Saimon, M. Rid, Metody sovremennoi matematicheskoi fiziki. T. 2. Garmonicheskii analiz. Samosopryazhennost, Mir, M., 1978 | MR

[10] Kh. Tsikon, R. Freze, V. Kirsh, B. Saimon, Operatory Shredingera s prilozheniyami k kvantovoi mekhanike i globalnoi geometrii, Mir, M., 1990 | MR

[11] D. Gilbarg, N. Trudinger, Ellipticheskie differentsialnye uravneniya v chastnykh proizvodnykh vtorogo poryadka, Nauka, M., 1989 | MR | Zbl

[12] V. V. Golubev, Lektsii po analiticheskoi teorii differentsialnykh uravnenii, GITTL, M., 1950 | MR

[13] M. Abramovits i I. Stigan (eds.), Spravochnik po spetsialnym funktsiyam, Nauka, M., 1979