On finiteness of discrete spectrum of three-particle Schrödinger operator on a lattice
M. I. MuminovUniversity of Technology Malaysia, Faculty of Science, UTM, Johor Bahru, Skudai, 81310, MalaysiaYo. M. ShermatovaSamarkand State University, Universitetskii bulv. 15, Samarkand, 140101, Republic of Uzbekistan
ABI
Аннотация
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 gravitational potentials. We prove the finiteness of a number of bound states of respective Schrödinger operator in a case, when potentials satisfy some conditions and zero is a regular point for two-particle sub-Hamiltonian. We find a set of values for particles masses values such that Schrödinger operator may have only finite number of eigenvalues lying to the left of essential spectrum.
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