M. I. Muminov, U. R. Shodiev, “On the essential spectrum of a four-particle Schrödinger operator on a lattice”, Mat. Tr., 2010, Volume 13, Number 1,Pages <nobr>169

On the essential spectrum of a four-particle Schrödinger operator on a lattice

M. I. Muminov^ab, U. R. Shodiev^a

^a A. Navoi Samarkand State University, Samarkand, Uzbekistan
^b Department of Mathematics, Dogus University, Istanbul, Turkey

Abstract: The Hamiltonian of a system of four arbitrary quantum particles with three-particle short-range interaction potentials on a three-dimensional lattice is examined. The location of the essential spectrum of this Hamiltonian is described by Faddeev's equations.

Key words: Schrödinger operator, Faddeev's equations, essential spectrum, compact operator, positive operator.

UDC: 517.984

Received: 12.02.2009