The existence of bound states in a system of three particles in an optical lattice

Abstract

We consider the hamiltonian of a system of three-particles (two identical fermions and one different particle) moving on the lattice interacting through repulsive or attractive zero-range pairwise potential . We prove for any the existence of bound states of the discrete three-particle Schrödinger operator being the three-particle quasi-momentum, associated to the hamiltonian .