Geodesic
Finiteness of the discrete spectrum of the Schrödinger operator of
Teoretičeskaâ i matematičeskaâ fizika, Tome 154 (2008) no. 2, pp. 363-371 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider a system of three quantum particles interacting by pairwise short-range attraction potentials on a three-dimensional lattice (one of the particles has an infinite mass). We prove that the number of bound states of the corresponding Schrödinger operator is finite in the case where the potentials satisfy certain conditions, the two two-particle sub-Hamiltonians with infinite mass have a resonance at zero, and zero is a regular point for the two-particle sub-Hamiltonian with finite mass.
Keywords: resonance, two-particle sub-Hamiltonian, discrete spectrum, variation principle. 
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     title = {Finiteness of the~discrete spectrum of {the~Schr\"odinger} operator of},
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M. I. Muminov. Finiteness of the discrete spectrum of the Schrödinger operator of. Teoretičeskaâ i matematičeskaâ fizika, Tome 154 (2008) no. 2, pp. 363-371. http://geodesic.mathdoc.fr/item/TMF_2008_154_2_a12/

[1] V. N. Efimov, YaF, 12:5 (1970), 1080–1091

[2] D. P. Yafaev, Matem. sb., 94(136):4(8) (1974), 567–593 | MR | Zbl

[3] A. V. Sobolev, Comm. Math. Phys., 156 (1993), 101–126 | DOI | MR | Zbl

[4] H. Tamura, J. Funct. Anal., 95 (1991), 433–459 | DOI | MR | Zbl

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

[6] M. E. Muminov, TMF, 148:3 (2006), 428–443 | DOI | MR | Zbl

[7] S. N. Lakaev, M. E. Muminov, TMF, 135:3 (2003), 478–503 | DOI | MR | Zbl

[8] P. Khalmosh, Gilbertovo prostranstvo v zadachakh, M., Mir, 1970 | MR | MR