The number of eigenvalues for an Hamiltonian in Fock space

Details The number of eigenvalues for an Hamiltonian in Fock space The number of eigenvalues for an Hamiltonian in Fock space

2005-01-12

arxiv.org/abs/math-ph/0501037v1

Physics

Mathematical Physics

23 pages

Scientific paper

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.

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