The Asymptotics of the Number of Eigenvalues of a Three-Particle Lattice Schrödinger Operator

The Hamiltonian of a system of three quantum-mechanical particles moving on the three-dimensional lattice \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathbb{Z}^3 $$ \end{document} and interacting via zero-range attractive potentials is considered. The location of the essential and discrete spectra of the three-particle discrete Schrödinger operator H(K), where K is the three-particle quasimomentum, is studied. The absence of eigenvalues below the bottom of the essential spectrum of H(K) for all sufficiently small values of the zero-range attractive potentials is established.