On compact perturbation of two-particle Schrödinger operator on a lattice

Abstract

We consider a system of two arbitrary quantum particles on three-dimensional lattice with certain dispersion functions (describing the transfer of the particle from one node to another) interacting by the attractive potential only on the nearest neighboring nodes. We find a class of potentials such that under perturbation of the two-particle operator h(k), corresponding to a two-particle system, with a potential from this class, the discrete spectrum of h(k) is preserved.