Existence of the eigenvalues of a tensor sum of the Friedrichs models with rank 2 perturbation
Tulkin H. RasulovBukhara State University, Bukhara, UzbekistanBekzod I. BahronovBukhara State University, Bukhara, Uzbekistan
ABI
Abstract
In the paper we consider a tensor sum H , , , > 0 of two Friedrichs models h , with rank two perturbation. The Hamiltonian H , is associated with a system of three quantum particles on one-dimensional lattice. We investigate the number and location of the eigenvalues of H , . The existence of eigenvalues located respectively inside, in the gap, and below the bottom of the essential spectrum of H , is proved.