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Dense point spectrum for the one-dimensional Dirac operator with an electrostatic potential

Published online by Cambridge University Press:  14 November 2011

Karl Michael Schmidt
Karl Michael Schmidt
Affiliation:
Mathematisches Institut der Universität, Theresienstraße 39, D-80333 München, Germany
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Abstract

For the one-dimensional Dirac operator, examples of electrostatic potentials with decay behaviour arbitrarily close to Coulomb decay are constructed for which the operator has a prescribed set of eigenvalues dense in the whole or part of its essential spectrum. A simple proof that the essential spectrum of one-dimensional Dirac operators with electrostatic potentials is never empty is given in the appendix.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 126 , Issue 5 , 1996 , pp. 1087 - 1096
Copyright
Copyright © Royal Society of Edinburgh 1996

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