This article is cited in 6 papers

On the discrete spectrum of Hamiltonians for pseudo-relativistic electrons

G. M. Zhislin^a, S. A. Vugal'ter

^a Scientific Research Institute of Radio Physics

Abstract: We consider the Hamiltonian $H$ of a system of $n$ pseudo-relativistic electrons in a Coulomb field of $n_0$ fixed nuclei. Under the assumption that the total charge of electrons and nuclei is non-negative, it is proved that the discrete spectrum of $H$ is infinite, and a spectral asymptotic formula is derived (without taking the Pauli exclusion principle into account). The results are extended to systems of the same type with long-range potentials more general than Coulomb potentials. It is also proved that the discrete spectrum is finite in the short-range case.

UDC: 517.9

MSC: 35P20, 35Q75, 46N50, 47N50, 70H05, 81Q10

Received: 09.01.2001

DOI: 10.4213/im372

 English version: Izvestiya: Mathematics, 2002, 66:1, 71–102

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