Geodesic
The~infiniteness of the~number of eigenvalues in the~gap in the~essential spectrum for the~three-particle Schr\"odinger operator on a~lattice
Teoretičeskaâ i matematičeskaâ fizika, Tome 159 (2009) no. 2, pp. 299-317

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We consider a system of three arbitrary quantum particles on a three-dimensional lattice that interact via attractive pair contact potentials. We find a condition for a gap to appear in the essential spectrum and prove that there are infinitely many eigenvalues of the Hamiltonian of the corresponding three-particle system in this gap.
Keywords: three-particle system on a lattice, Schrödinger operator, essential spectrum, discrete spectrum, compact operator. 
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     author = {M. I. Muminov},
     title = {The~infiniteness of the~number of eigenvalues in the~gap in the~essential spectrum for the~three-particle {Schr\"odinger} operator on a~lattice},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {299--317},
     publisher = {mathdoc},
     volume = {159},
     number = {2},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2009_159_2_a8/}
}
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M. I. Muminov. The~infiniteness of the~number of eigenvalues in the~gap in the~essential spectrum for the~three-particle Schr\"odinger operator on a~lattice. Teoretičeskaâ i matematičeskaâ fizika, Tome 159 (2009) no. 2, pp. 299-317. http://geodesic.mathdoc.fr/item/TMF_2009_159_2_a8/