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Zeitschrift für Naturforschung A

A Journal of Physical Sciences

Editor-in-Chief: Holthaus, Martin

Editorial Board: Fetecau, Corina / Kiefer, Claus

12 Issues per year

IMPACT FACTOR 2016: 1.432

CiteScore 2017: 1.30

SCImago Journal Rank (SJR) 2017: 0.403
Source Normalized Impact per Paper (SNIP) 2017: 0.632

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Volume 49, Issue 11


Scalar Potentials and the Dirac Equation

Bastian Bergerhoff
  • Gesellschaft für Schwerionenforschung (GSI), Planckstraße 1, Postfach 110 552, D-64220 Darmstadt, Federal Republic of Germany
  • Other articles by this author:
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/ Gerhard Soff
  • Institut für Theoretische Physik, Technische Universität, 01062 Dresden, Federal Republic of Germany
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Published Online: 2014-06-02 | DOI: https://doi.org/10.1515/zna-1994-1101


The Dirac equation is solved for various types of scalar potentials. Energy eigenvalues and normalized bound-state wave functions are calculated analytically for a scalar 1 / r-potential as well as for a mixed scalar and Coulomb 1 / r-potential. Also continuum wave functions for positive and negative energies are derived. Similarly, we investigate the solutions of the Dirac equation for a scalar square-well potential. Relativistic wave functions for scalar Yukawa and exponential potentials are determined numerically. Finally, we also discuss solutions of the Dirac equation for scalar linear and quadratic potentials which are frequently used to simulate quark confinement.

About the article

Received: 1994-10-05

Published Online: 2014-06-02

Published in Print: 1994-11-01

Citation Information: Zeitschrift für Naturforschung A, Volume 49, Issue 11, Pages 997–1012, ISSN (Online) 1865-7109, ISSN (Print) 0932-0784, DOI: https://doi.org/10.1515/zna-1994-1101.

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© 1946 – 2014: Verlag der Zeitschrift für Naturforschung. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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