The infiniteness of the number of eigenvalues in the gap in the essential spectrum for the three-particle Schrodinger operator on a lattice

摘要

We consider a system of three arbitrary quantum particles on a three-dimensional lattice that interact via attractive pair contact potentials. We find a condition for a gap to appear in the essential spectrum and prove that there are infinitely many eigenvalues of the Hamiltonian of the corresponding three-particle system in this gap.