Abstract
In this paper, the Hamiltonian of the system of two fermions on the three-dimensional lattice ℤ3 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 H0(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.
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