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A MINIMAX PRINCIPLE FOR THE EIGENVALUES IN SPECTRAL GAPS

Published online by Cambridge University Press:  01 October 1999

MARCEL GRIESEMER  and
HEINZ SIEDENTOP
MARCEL GRIESEMER
Affiliation:
Mathematik, Universität Regensburg, D-93040 Regensburg, Germany; [email protected], [email protected]
HEINZ SIEDENTOP
Affiliation:
Mathematik, Universität Regensburg, D-93040 Regensburg, Germany; [email protected], [email protected]
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Abstract

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.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 60 , Issue 2 , October 1999 , pp. 490 - 500
Copyright
The London Mathematical Society 1999

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