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Spectra of Hamiltonians of molecule pseudorelativistic electrons in spaces of functions with permutational and point symmetry

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Abstract

We study the spectral properties of the Hamiltonian H n of n pseudorelativistic electrons in the Coulomb field of k fixed nuclei in spaces of functions having arbitrary given types of permutational and point symmetry. For this operator, we establish the location of the essential spectrum, obtain two-sided estimates of the discrete spectrum counting function in terms of the counting functions of the discrete spectrum of some two-particle nonrelativistic operators, and find the leading term of the spectral asymptotics.

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Authors and Affiliations

  1. Nizhnii Novgorod Institute of Radiophysical Research, Russia

    G. M. Zhislin

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  1. G. M. Zhislin
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__________

Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 40, No. 2, pp. 65–69, 2006

Original Russian Text Copyright © by G. M. Zhislin

The research was supported by RFBR grant No. 03-01-00715.

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Zhislin, G.M. Spectra of Hamiltonians of molecule pseudorelativistic electrons in spaces of functions with permutational and point symmetry. Funct Anal Its Appl 40, 134–138 (2006). https://doi.org/10.1007/s10688-006-0020-5

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  • DOI: https://doi.org/10.1007/s10688-006-0020-5

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