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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
Affiliation:
Mathematisches Institut der Universität, Theresienstraße 39, D-80333 München, Germany

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
Copyright
Copyright © Royal Society of Edinburgh 1996

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