ON THE THEORY OF THE DISCRETE SPECTRUM OF THE THREE-PARTICLE SCHRÖDINGER OPERATOR

Abstract

We investigate the discrete spectrum of the Schrödinger operator H for a system of three particles. We assume that the operators hα, α = 1, 2, 3, which describe the three subsystems of two particles do not have any negative eigenvalues. Under the assumption that either two or three of the operators hα have so-called virtual levels at the start of the continuous spectrum, we establish the existence of an infinite discrete spectrum for the three-particle operator H. The functions which describe the interactions between pairs of particles can be rapidly decreasing (or even of compact support) with respect to x. Bibliography: 17 items.

Identifiers

DOI

10.1070/sm1974v023n04abeh001730

Citations and references