Existence condition of an eigenvalue of the three particle Schr¨odinger operator on a lattice

Abstract

We consider the three-particle discrete Schrodinger operator Hµ,γ(К), К ϵТ3 associated to a system of three particles (two particle are fermions with mass 1 and third one is an another particle with mass m = 1/y < 1) interacting through zero range pairwise potential µ> 0 on the three-dimensional lattice Z3. It is proved that for γϵ(1, γ0) (γ0≈4,7655) the operator Hµ,γ(π), π=(π,π,π), has no eigenvalue and has only unique eigenvalue with multiplicity three for γ>γ0 lying right of the essential spectrum for sufficiently large µ.