A MINIMAX PRINCIPLE FOR THE EIGENVALUES IN SPECTRAL GAPS

A minimax principle is derived for the eigenvalues in the spectral gap of a possibly non-semibounded self-adjoint operator. It allows the nth eigenvalue of the Dirac operator with Coulomb potential from below to be bound by the nth eigenvalue of a semibounded Hamiltonian which is of interest in the...

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Bibliographic Details
Published in:Journal of the London Mathematical Society 1999-10, Vol.60 (2), p.490-500
Main Authors: GRIESEMER, MARCEL, SIEDENTOP, HEINZ
Format: Article
Language:English
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Summary:A minimax principle is derived for the eigenvalues in the spectral gap of a possibly non-semibounded self-adjoint operator. It allows the nth eigenvalue of the Dirac operator with Coulomb potential from below to be bound by the nth eigenvalue of a semibounded Hamiltonian which is of interest in the context of stability of matter. As a second application it is shown that the Dirac operator with suitable non-positive potential has at least as many discrete eigenvalues as the Schrödinger operator with the same potential.
ISSN:0024-6107
1469-7750
DOI:10.1112/S0024610799007930