On the Number of Eigenvalues of the Lattice Model Operator in One-Dimensional Case

It is considered a model operator h(mu) (k), k is an element of T (-pi, pi], corresponding to the Hamiltonian of systems of two arbitrary quantum particles on a one-dimensional lattice with a special dispersion function that describes the transfer of a particle from one site to another interacting by a some short-range attraction potential v(mu), mu = (mu(0), mu(1), mu(2), mu(3)) is an element of R-+(4). The number of eigenvalues of the operator h(mu) (k), k is an element of T depending on the energy of the particle interaction vector mu is an element of R-+(4) and the total quasi-momentum k is an element of T is studied.