Spectral properties of a two-particle hamiltonian on a d-dimensional lattice

A system of two arbitrary quantum particles moving on d-dimensional lattice interacting via some attractive potential is considered. The number of eigenvalues of the family h(k) is studied depending on the interaction energy of particles and the total quasi-momentum k T d (T dd-dimensional torus). Depending on the interaction energy, the conditions for h(0) that has simple or multifold virtual level at 0 are found.

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