Advances in Imaging and Electron Physics

Dirac's Difference Equation and the Physics of Finite Differences

Series Editor:

  • Peter Hawkes, CEMES/Laboratoire d'Optique Electronique du Centre National de la Recherche Scientifique, Toulouse, France


  • Henning Harmuth, Retired, The Catholic University of America, Washington, DC, USA
  • Beate Meffert, Humboldt University, Berlin, Germany

In this volume, the authors extend the calculus of finite differences to Dirac's equation. They obtain solutions for particles with negative mass that are completely equivalent to the solutions with positive mass. In addition, they obtain solutions for nuclear distances of the order of 10-13m and less rather than for the usual atomic distances. They report a number of other deviations from the differential theory, for instance they found a slight deviation in the eigenvalues of an electron in a Coulomb field, similar to the Lamb shift. In two sections some surprising results are shown for the concept of space caused by the replacement of dx by delta x.
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Physicists, electrical engineers and applied mathematicians in all branches of image processing and microscopy as well as electron physics in general


Book information

  • Published: November 2008
  • ISBN: 978-0-12-374221-6

Table of Contents

PrefaceFuture ContributionsDedicationForewordList of Frequently Used Symbols1. Introduction2. Modified Dirac Equation3. Inhomogeneous Dirac Difference Equation4. Dirac Difference Equation in Spherical Coordinates5. Inhomogeneous Equations for Coulomb Potential6. AppendixReferences and BibliographyIndex