Geodesic
On the discrete spectrum of Hamiltonians for pseudo-relativistic electrons
Izvestiya. Mathematics , Tome 66 (2002) no. 1, pp. 71-102

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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. 
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     author = {G. M. Zhislin and S. A. Vugal'ter},
     title = {On the discrete spectrum of {Hamiltonians} for pseudo-relativistic electrons},
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     url = {http://geodesic.mathdoc.fr/item/IM2_2002_66_1_a3/}
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G. M. Zhislin; S. A. Vugal'ter. On the discrete spectrum of Hamiltonians for pseudo-relativistic electrons. Izvestiya. Mathematics , Tome 66 (2002) no. 1, pp. 71-102. http://geodesic.mathdoc.fr/item/IM2_2002_66_1_a3/