Formula for the number of eigenvalues of a three-particle Schr?dinger operator on a lattice

摘要

We consider a system of three arbitrary quantum particles on a three-dimensional lattice that interact via short-range attractive potentials. We obtain a formula for the number of eigenvalues in an arbitrary interval outside the essential spectrum of the three-particle discrete Schr?dinger operator and find a sufficient condition for the discrete spectrum to be finite. We give an example of an application of our results.