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

We consider the three-particle discrete Schrodinger operator H µ ,γ ( К ), К ϵТ 3 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 Z 3 . It is proved that for γϵ(1, γ 0 ) (γ 0 ≈4,7655) the operator H µ,γ ( π ), π =(π,π,π), has no eigenvalue and has only unique eigenvalue with multiplicity three for γ>γ 0 lying right of the essential spectrum for sufficiently large µ.

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