Spectral features of two-particle schr–dinger operator on d-dimensiional lattice

Abstract

This paper reports the spectral features of two-particle Schrödinger Hamiltonian operator on d-dimensional lattice Zd. A family of operators h(k) was emanated after the “separation of the center of mass” of a system of two particles depending on the values of total quasimomentum k∈Td, (where Td is d-dimensional torus). A sufficiency condition was achieved for the finiteness of the number of embedded and discrete eigenvalues of h(k) for any fixed k∈Td.