Essential and Point Spectrum of a Model Hamiltonian Associated with the Three-particle Quantum Systems on a Lattice

In this paper, we investigate the tensor sum Hμ,λ with μ,λ>0 , constructed from two Friedrichs models perturbed by rank two operators. The Hamiltonian Hμ,λ describes a system of three quantum particles on a d-dimensional lattice. We define a set of parameters μ and λ such that the essential spectrum of the Hamiltonian Hμ,λ is given by the union of one, two, or three closed intervals. The point spectrum of the Hamiltonian Hμ,λ is investigated through finite integrals appearing in the Fredholm determinant associated with the Friedrichs model.