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