The discrete spectrum of the three-particle Schrödinger operator on $\mathbb{Z}^2$

Abstract

We study a three-particle lattice Hamiltonian describing two identical bosons and one fermion on $\mathbb{Z}^2$, interacting via attractive or repulsive zero-range pair potentials. We analyze the point spectrum of the associated three-particle lattice discrete Schrödinger operator and describe the existence and multiplicity of bound states. Particular attention is devoted to the case in which the bosons have infinite mass.