Geodesic
Localization of the essential spectrum of the energy operators of $n$-particle quantum systems in a magnetic field
Teoretičeskaâ i matematičeskaâ fizika, Tome 97 (1993) no. 1, pp. 94-112 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Theorems on the localization of the essential spectrum of given $SO(2)$ symmetry for $n$-particle Hamiltonians in an external magnetic field are proved. The energy operators are studied for systems of arbitrary particles in the absence of an external potential field and for systems of identical particles in an external potential field. Some of the results were announced in earlier papers [1, 2]. 
@article{TMF_1993_97_1_a6,
     author = {S. A. Vugal'ter and G. M. Zhislin},
     title = {Localization of the essential spectrum of the energy operators of $n$-particle quantum systems in a~magnetic field},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {94--112},
     year = {1993},
     volume = {97},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1993_97_1_a6/}
}
TY  - JOUR
AU  - S. A. Vugal'ter
AU  - G. M. Zhislin
TI  - Localization of the essential spectrum of the energy operators of $n$-particle quantum systems in a magnetic field
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1993
SP  - 94
EP  - 112
VL  - 97
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1993_97_1_a6/
LA  - ru
ID  - TMF_1993_97_1_a6
ER  - 
%0 Journal Article
%A S. A. Vugal'ter
%A G. M. Zhislin
%T Localization of the essential spectrum of the energy operators of $n$-particle quantum systems in a magnetic field
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1993
%P 94-112
%V 97
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1993_97_1_a6/
%G ru
%F TMF_1993_97_1_a6
S. A. Vugal'ter; G. M. Zhislin. Localization of the essential spectrum of the energy operators of $n$-particle quantum systems in a magnetic field. Teoretičeskaâ i matematičeskaâ fizika, Tome 97 (1993) no. 1, pp. 94-112. http://geodesic.mathdoc.fr/item/TMF_1993_97_1_a6/

[1] Vugalter S. A., Zhislin G. M., Funkts. analiz i ego prilozh., 25:4 (1991), 83–86 | MR | Zbl

[2] Vugalter S. A., Zhislin G. M., DAN SSSR, 317:6 (1991), 1365–1369 | MR

[3] Avron J. E., Herbert J. W., Simon B., Ann. Phys., 114 (1978), 431 | DOI | MR | Zbl

[4] Rid M., Saimon B., Metody sovremennoi matematicheskoi fiziki. Analiz operatorov, Mir, M., 1982 | MR

[5] Vugalter S. A., Zhislin G. M., Algebra i analiz, 3:6 (1991), 119–154 | MR | Zbl

[6] Antonets M. A., Zhislin G. M., Shereshevskii I. A., “O diskretnom spektre $N$-chastichnykh gamiltonianov”, prilozhenie k kn.: Iorgens K., Vaidman I., Spektralnye svoistva gamiltonovykh operatorov, Mir, M., 1976 | MR

[7] Avron J. E., Herbert J. W., Simon B., Duke, Math. J., 45 (1978), 847 | MR | Zbl

[8] Sigalov A. G., Sigal I. M., TMF, 5:1 (1970), 73–93 | MR

[9] Vugalter S. A., Zhislin G. M., TMF, 55:1 (1983), 66–77 | MR

[10] Vugal'ter S. A., Zhislin G. M., ROMP, 19:1 (1984), 39–90 | MR | Zbl