Asymptotics of eigenvalues of two-particle Schrödinger operators on lattices with zero range interaction

Abstract

The Hamiltonian of a system of two quantum-mechanical particles moving on the d-dimensional lattice and interacting via zero-range attractive pair potentials is considered. For the two-particle energy operator —the two-particle quasi-momentum—the existence of a unique positive eigenvalue z(μ, K) above the upper edge of the essential spectrum of Hμ(K) is proven and asymptotics for z(μ, K) are found when μ approaches to some μ0(K) and K → 0.