Bound states of the system of two fermions on the three-dimensional lattice

In this paper, the Hamiltonian of the system of two fermions on the three-dimensional lattice Z(3) is considered. Under some conditions to the potential, it is proven that H(k) has four invariant subspaces: in one of them H(k) coincides with H-0(k) and the restrictions of H(k) to the rests three subspaces are unitarily equivalent to each other. Moreover, for the eigenvalues and eigenfunctions of these restricted operators explicit expressions are found.