Universality of the discrete spectrum asymptotics of the three-particle Schrödinger operator on a lattice

Abstract

In the present paper, we consider the Hamiltonian H(K), K ∈ T := (−π;π] of a system of three arbitrary quantum mechanical particles moving on the three-dimensional lattice and interacting via zero range potentials. We find a finite set Λ ⊂ T such that for all values of the total quasi-momentum K ∈ Λ the operator H(K) has infinitely many negative eigenvalues accumulating at zero. It is found that for every K ∈ Λ, the number N(K; z) of eigenvalues of H(K) lying on the left of z, z < 0, satisfies the asymptotic relation