The existence of eigenvalues of Schrödinger operator on a lattice in the gap of the essential spectrum
J. I. AbdullaevSamarkand State University, University Boulevard 15, Samarkand 140104, UzbekistanA. M. KhalkhuzhaevSamarkand State University, University Boulevard 15, Samarkand 140104, Uzbekistan
ABI
Abstract
Abstract We consider a three-particle discrete Schrödinger operator H μγ (K), K 2 T 3 associated to a system of three particles (two fermions and one different particle) interacting through zero range pairwise potential μ > 0 on the three-dimensional lattice Z 3 . It is proved that the operator H μγ (K), ||K|| < δ, for γ > γ 0 has at least two eigenvalues in the gap of the essential spectrum for sufficiently large μ > 0.