The existence of eigenvalues of Schrödinger operator on a lattice in the gap of the essential spectrum

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.

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