THE FINITENESS OF THE NUMBER OF EIGENVALUES OF THE FOUR-PARTICLE SCHRÖDINGER OPERATOR WITH THREE-PARTICLE CONTACT INTERACTION

Abstract

In this paper, we consider the four-particle Schr\"{o}dinger operator corresponding to the Hamiltonian of a system of four arbitrary quantum particles via a three-particle contact interaction potential on a three-dimensional lattice. The finiteness of the number of eigenvalues of the Schr\"{o}dinger operator lying to the left of the essential spectrum for zero value of the total quasi-momentum is proved.