On the finiteness of the discrete spectrum of the three-particle Schrödinger operator
Teoretičeskaâ i matematičeskaâ fizika, Tome 25 (1975) no. 2, pp. 185-195 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The Schrödinger operator $H$ of a three-particle system with two-body interactions in considered. Under the assumptions that two-particle subsystems do not possess any negative eigenvalues and one of the subsystems has a virtual state at the lower bound of the continuous spectrum, the proof of the finiteness of discrete spectrum of operator $H$ is performed.
@article{TMF_1975_25_2_a3,
     author = {D. R. Yafaev},
     title = {On the finiteness of the discrete spectrum of the three-particle {Schr\"odinger} operator},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {185--195},
     year = {1975},
     volume = {25},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1975_25_2_a3/}
}
TY  - JOUR
AU  - D. R. Yafaev
TI  - On the finiteness of the discrete spectrum of the three-particle Schrödinger operator
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1975
SP  - 185
EP  - 195
VL  - 25
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1975_25_2_a3/
LA  - ru
ID  - TMF_1975_25_2_a3
ER  - 
%0 Journal Article
%A D. R. Yafaev
%T On the finiteness of the discrete spectrum of the three-particle Schrödinger operator
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1975
%P 185-195
%V 25
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1975_25_2_a3/
%G ru
%F TMF_1975_25_2_a3
D. R. Yafaev. On the finiteness of the discrete spectrum of the three-particle Schrödinger operator. Teoretičeskaâ i matematičeskaâ fizika, Tome 25 (1975) no. 2, pp. 185-195. http://geodesic.mathdoc.fr/item/TMF_1975_25_2_a3/

[1] D. R. Yafaev, DAN SSSR, 206 (1972), 68

[2] G. M. Zhislin, DAN SSSR, 207 (1972), 25 | Zbl

[3] D. R. Yafaev, Matem. sb., 94 (1974), 567 | MR | Zbl

[4] V. N. Efimov, Phys. Lett., B33 (1970), 563 | DOI

[5] L. D. Faddeev, Trudy MIAN SSSR, 69, 1963 | MR | Zbl

[6] D. R. Yafaev, Matem. voprosy teorii rasprostraneniya voln. 7, Zapiski nauchnykh seminarov LOMI, 51, 1975, 203–216 | Zbl

[7] S. Weinberg, Phys. Rev., B133 (1964), 232 | DOI | MR