Asymptotic behavior of an eigenvalue of the two-particle discrete Schr?dinger operator

摘要

We consider a two-particle discrete Schr?dinger operator corresponding to a system of two identical particles on a lattice interacting via an attractive pairwise zero-range potential. We show that there is a unique eigenvalue below the bottom of the essential spectrum for all values of the coupling constant and two-particle quasimomentum. We obtain a convergent expansion for the eigenvalue.