THE NUMBER OF EIGENVALUES OF THE TWO-PARTICLE DISCRETE SCHR¨ODINGER OPERATOR

摘要

We consider the two-particle discrete Schr¨odinger operator associated with the Hamiltonian of a system of two particles (fermions) interacting only at the nearest neighbor sites. We find the number and the location of the eigenvalues of this operator depending on the particle interaction energy, the system quasimomentum, and the dimension of the lattice Zν, ν ≥ 1.