On the Discrete Spectrum of the Three-Particle Schrödinger Operator on a Two-Dimensional Lattice
Zahriddin MuminovRomanovskii Institute of Mathematics, Academy of Sciences of Uzbekistan, 100174, Tashkent, UzbekistanN. M. AlievNational University of Uzbekistan, 100174, Tashkent, UzbekistanTirkash RadjabovSamarkand State University, Faculty of Mathematics, 140104, Samarkand, Uzbekistan
ABI
Abstract
We consider Schrödinger operator corresponding to the Hamiltonian of a system of three arbitrary particles on the two-dimensional lattice, where the particles interact pairwise via zero-range (contact) attractive potentials. We prove that the discrete spectrum of the Schrödinger operator is infinite, if the masses of two particles in a three-particle system are infinite.
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