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Some essentially self-adjoint Dirac operators with spherically symmetric potentials

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Abstract

It is shown that the one electron Dirac operator in a stationary electric field is essentially self-adjoint, on the domain of infinitely differentiable functions of compact support, for a class of spherically symmetric potentials including the Coulomb potential, for atomic numbers less than or equal to 118. In addition, the domain of the closure of the perturbed operator is the same as the domain of the closure of the unperturbed operator. We also give an abstract theorem on domain-preserving essential self-adjointness for perturbed operators, which is perhaps of independent interest.

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Authors and Affiliations

  1. University of Colorado, Colorado

    K. E. Gustafson & P. A. Rejto

  2. University of Minnesota, Minnesota, USA

    K. E. Gustafson & P. A. Rejto

Authors
  1. K. E. Gustafson
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  2. P. A. Rejto
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Additional information

This work was initiated while both authors were guests of the Institute for Theoretical Physics, University of Geneva, Switzerland.

Partially supported by N.S.F. Grant G. P. 15239 A1

Supported by N. S. F. Grant G. P. 28933.

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Gustafson, K.E., Rejto, P.A. Some essentially self-adjoint Dirac operators with spherically symmetric potentials. Israel J. Math. 14, 63–75 (1973). https://doi.org/10.1007/BF02761535

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  • DOI: https://doi.org/10.1007/BF02761535

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