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. 
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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/

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