Geodesic
On the discrete spectrum of the Hamiltonian of an $n$-particle quantum system
Teoretičeskaâ i matematičeskaâ fizika, Tome 16 (1973) no. 2, pp. 235-246 
M. A. Antonets; G. M. Zhislin; I. A. Shereshevskii. On the discrete spectrum of the Hamiltonian of an $n$-particle quantum system. Teoretičeskaâ i matematičeskaâ fizika, Tome 16 (1973) no. 2, pp. 235-246. http://geodesic.mathdoc.fr/item/TMF_1973_16_2_a9/
@article{TMF_1973_16_2_a9,
     author = {M. A. Antonets and G. M. Zhislin and I. A. Shereshevskii},
     title = {On the discrete spectrum of the {Hamiltonian} of an $n$-particle quantum system},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {235--246},
     year = {1973},
     volume = {16},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1973_16_2_a9/}
}
TY  - JOUR
AU  - M. A. Antonets
AU  - G. M. Zhislin
AU  - I. A. Shereshevskii
TI  - On the discrete spectrum of the Hamiltonian of an $n$-particle quantum system
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1973
SP  - 235
EP  - 246
VL  - 16
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1973_16_2_a9/
LA  - ru
ID  - TMF_1973_16_2_a9
ER  - 
%0 Journal Article
%A M. A. Antonets
%A G. M. Zhislin
%A I. A. Shereshevskii
%T On the discrete spectrum of the Hamiltonian of an $n$-particle quantum system
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1973
%P 235-246
%V 16
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1973_16_2_a9/
%G ru
%F TMF_1973_16_2_a9

Voir la notice de l'article provenant de la source Math-Net.Ru

Sufficient conditions are obtained for the discrete spectrum of the energy operator of an $n$-particle system to be finite in the space of functions of given permutational and rotational symmetry. It is shown that under the same conditions the boundary of the continuous speetrum cannot be an eigenvalue of infinite multiplicity. For application of the basic theorem, the etgenvatues of the Schrödinger operator are investigated as functions of the coupling constant.

[1] J. Uchiyama, Publ. RIMS, Kyoto Univ., ser. A, 5 (1969), 51 | DOI | MR | Zbl

[2] J. Uchiyama, Publ. RIMS, Kyoto Univ., ser. A, 6 (1970), 193 | DOI | MR | Zbl

[3] G. M. Zhislin, TMF, 7 (1971), 332 | Zbl

[4] K. Jörgens, Über das wesentliche Spectrum elliptischen Differentialgleichungen von Schrödinger-Typ, Univ. of Heidelberg Tech. Report, 1965 | Zbl

[5] A. G. Sigalov, I. M. Sigal, TMF, 5 (1970), 73 | MR

[6] B. Simon, Helv. Phys. Acta, 43 (1970), 607 | MR

[7] N. Burbaki, Funktsii deistvitelnogo peremennogo, «Nauka», 1965 | MR

[8] F. Riss, S. Nad, Lektsii po funktsionalnomu analizu, IL, 1954 | MR

[9] G. M. Zhislin, A. G. Sigalov, Izv. AN SSSR, ser. matem., 29:6 (1965), 1261–1272 | MR | Zbl