Sergio Albeverio, Saidakhmat N. Lakaev, Tulkin H. Rasulov
Published 2005-01-12Version 1
A model operator $H$ corresponding to the energy operator of a system with non-conserved number $n\leq 3$ of particles is considered. The precise location and structure of the essential spectrum of $H$ is described. The existence of infinitely many eigenvalues below the bottom of the essential spectrum of $H$ is proved if the generalized Friedrichs model has a virtual level at the bottom of the essential spectrum and for the number $N(z)$ of eigenvalues below $z<0$ an asymptotics established. The finiteness of eigenvalues of $H$ below the bottom of the essential spectrum is proved if the generalized Friedrichs model has a zero eigenvalue at the bottom of its essential spectrum.
On the Spectrum of a Model Operator in Fock Space
The Faddeev Equation and Essential Spectrum of a Hamiltonian in Fock Space
On the essential and discrete spectrum of a model operator related to three-particle discrete Schrödinger operators
