Geodesic
Discrete spectrum of a noncompact perturbation of a three-particle Schrödinger operator on a lattice
Teoretičeskaâ i matematičeskaâ fizika, Tome 182 (2015) no. 3, pp. 435-452 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider a system of three arbitrary quantum particles on a three-dimensional lattice interacting via attractive pair-contact potentials and attractive potentials of particles at the nearest-neighbor sites. We prove that the Hamiltonian of the corresponding three-particle system has infinitely many eigenvalues. We also list different types of attractive potentials whose eigenvalues can be to the left of the essential spectrum, in a gap in the essential spectrum, and in the essential spectrum of the considered operator.
Keywords: three-particle system on a lattice, Schrödinger operator, asymptotic number of eigenvalues, infinitely many eigenvalues in a gap in the essential spectrum, infinitely many eigenvalues in the essential spectrum. 
@article{TMF_2015_182_3_a3,
     author = {M. I. Muminov and N. M. Aliev},
     title = {Discrete spectrum of a~noncompact perturbation of a~three-particle {Schr\"odinger} operator on a~lattice},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2015_182_3_a3/}
}
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M. I. Muminov; N. M. Aliev. Discrete spectrum of a noncompact perturbation of a three-particle Schrödinger operator on a lattice. Teoretičeskaâ i matematičeskaâ fizika, Tome 182 (2015) no. 3, pp. 435-452. http://geodesic.mathdoc.fr/item/TMF_2015_182_3_a3/

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