Geodesic
On finiteness of discrete spectrum of three-particle Schr\"odinger operator on a~lattice
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2016), pp. 27-35

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On three-dimensional lattice we consider a system of three quantum particles (two of them are identical (fermions) and the third one is of another nature) that interact with the help of paired short-range potentials of attraction. We prove the finiteness of a number of bound states of respective Schrödinger operator in a case when potentials satisfy some conditions and the zero is a regular point for two-particle subhamiltonian. We find a set of particles masses' values such that the Schrödinger operator may have only finite number of eigenvalues lying to the left from essential spectrum.
Keywords: three-particle system on a lattice, Schrödinger operator, essential spectrum, discrete spectrum, Vineberg equation, virtual level. 
@article{IVM_2016_1_a2,
     author = {M. E. Muminov and E. M. Shermatova},
     title = {On finiteness of discrete spectrum of three-particle {Schr\"odinger} operator on a~lattice},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {27--35},
     publisher = {mathdoc},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2016_1_a2/}
}
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M. E. Muminov; E. M. Shermatova. On finiteness of discrete spectrum of three-particle Schr\"odinger operator on a~lattice. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2016), pp. 27-35. http://geodesic.mathdoc.fr/item/IVM_2016_1_a2/