On the number of eigenvalues of a model operator on a one-dimensional lattice

Abstract

A model operator hμ(k), k∈(-π,π], corresponding to the Hamiltonian of a system of two arbitrary quantum particles on a one-dimensional lattice with a special dispersion function is considered. The function describes the transfer of a particle from site to sites interacting using a short-range attraction potential νμ, μ = (μ0,μ1,μ2,μ3) ∈ ℝ+4. The detailed descriptions of changes in the number of eigenvalues of the energy operator hμ(k), k∈(-π,π], relative to values of the particle interaction vector and the total quasi-momentum k ∈ Т of the system of two particles is presented.