The number of eigenvalues for an Hamiltonian in Fock space
Sergio Albeverio, Saidakhmat N. Lakaev, Tulkin H. Rasulov
Abstract
A model operator H corresponding to the energy operator of a system with non-conserved number n≤ 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.
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