Geodesic
Finiteness of the Discrete Spectrum of the Hamiltonian of a System of Three Arbitrary Particles on a Lattice
Teoretičeskaâ i matematičeskaâ fizika, Tome 129 (2001) no. 3, pp. 415-431 
S. N. Lakaev; S. M. Samatov. Finiteness of the Discrete Spectrum of the Hamiltonian of a System of Three Arbitrary Particles on a Lattice. Teoretičeskaâ i matematičeskaâ fizika, Tome 129 (2001) no. 3, pp. 415-431. http://geodesic.mathdoc.fr/item/TMF_2001_129_3_a4/
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     title = {Finiteness of the {Discrete} {Spectrum} of the {Hamiltonian} of a {System} of {Three} {Arbitrary} {Particles} on a {Lattice}},
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We prove that the number of bound states for the Hamiltonian of a system of three arbitrary particles interacting through pairwise attraction potentials on a three-dimensional lattice is finite in the cases where (1) none of the two-particle subsystems has a virtual level and (2) only one of the two-particle subsystems has a virtual level.

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

[2] G. M. Zhislin, DAN SSSR, 207:1 (1972), 25 | MR | Zbl

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

[4] Yu. N. Ovchinnikov, I. M. Sigal, Ann. Phys., 123 (1989), 274 | DOI | MR

[5] H. J. Tamura, Funct. Anal., 95 (1991), 433 | DOI | MR | Zbl

[6] A. V. Sobolev, Commun. Math. Phys., 156 (1993), 101 | DOI | MR | Zbl

[7] V. N. Efimov, YaF, 12:5 (1970), 1080

[8] D. R. Yafaev, TMF, 25:2 (1975), 185 | MR | Zbl

[9] S. A. Vugalter, G. M. Zhislin, Trudy MMO, 49, 1986, 92 | MR

[10] D. C. Mattis, Rev. Modern. Phys., 58:2 (1986), 361 | DOI | MR

[11] A. I. Mogilner, “The problem of a few quasi-particles in solid-state physics”, Applications of Self-Adjoint Extensions in Quantum Physics, Lect. Notes Phys., 324, eds. P. Exner, P. Šeba, Springer, Berlin, 1988, 160 | DOI | MR

[12] S. N. Lakaev, TMF, 89:1 (1991), 94 | MR

[13] S. N. Lakaev, Funkts. analiz i ego prilozh., 27:3 (1993), 15 | MR | Zbl

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