Spectral Features of Two-Particle Schrödinger Operator on d-Dimensiional Lattice

Abstract

This paper reports the spectral features of two-particle Schrodinger Hamiltonian operator on d-dimensional lattice $${{\mathbb {Z}}}^d$$. 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 $$k\in {{\mathbb {T}}}^d$$, (where $${{\mathbb {T}}}^d$$ 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 $$k\in {{\mathbb {T}}}^d.$$