Abstract:
We consider a system of three arbitrary quantum particles on a three-dimensional lattice interacting via attractive pair-contact potentials and attractive potentials of particles at the nearest-neighbor sites. We prove that the Hamiltonian of the corresponding three-particle system has infinitely many eigenvalues. We also list different types of attractive potentials whose eigenvalues can be to the left of the essential spectrum, in a gap in the essential spectrum, and in the essential spectrum of the considered operator.
Keywords:three-particle system on a lattice, Schrödinger operator, asymptotic number of eigenvalues, infinitely many eigenvalues in a gap in the essential spectrum, infinitely many eigenvalues in the essential spectrum.