Advances in Imaging and Electron Physics, Volume 154

1st Edition

Dirac's Difference Equation and the Physics of Finite Differences

Authors: Henning Harmuth Beate Meffert
Serial Editors: Peter Hawkes
Hardcover ISBN: 9780123742216
eBook ISBN: 9780080880365
Imprint: Academic Press
Published Date: 7th November 2008
Page Count: 336
260.00 + applicable tax
160.00 + applicable tax
200.00 + applicable tax
231.00 + applicable tax
Compatible Not compatible
VitalSource PC, Mac, iPhone & iPad Amazon Kindle eReader
ePub & PDF Apple & PC desktop. Mobile devices (Apple & Android) Amazon Kindle eReader
Mobi Amazon Kindle eReader Anything else

Institutional Access

Table of Contents

Preface Future Contributions Dedication Foreword List of Frequently Used Symbols

  1. Introduction
  2. Modified Dirac Equation
  3. Inhomogeneous Dirac Difference Equation
  4. Dirac Difference Equation in Spherical Coordinates
  5. Inhomogeneous Equations for Coulomb Potential
  6. Appendix References and Bibliography Index


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.


Physicists, electrical engineers and applied mathematicians in all branches of image processing and microscopy as well as electron physics in general


No. of pages:
© Academic Press 2008
Academic Press
eBook ISBN:
Hardcover ISBN:

About the Authors

Henning Harmuth Author

Affiliations and Expertise

Retired, The Catholic University of America, Washington, DC, USA

Beate Meffert Author

Affiliations and Expertise

Humboldt University, Berlin, Germany

About the Serial Editors

Peter Hawkes Serial Editor

Peter Hawkes graduated from the University of Cambridge and subsequently obtained his PhD in the Electron Microscopy Section of the Cavendish Laboratory. He remained there for several years, working on electron optics and digital image processing before taking up a research position in the CNRS Laboratory of Electron Optics (now CEMES-CNRS) in Toulouse, of which he was Director in 1987. During the Cambridge years, he was a Research Fellow of Peterhouse and a Senior Research fellow of Churchill College. He has published extensively, both books and scientific journal articles, and is a member of the editorial boards of Ultramicroscopy and the Journal of Microscopy. He was the founder-president of the European Microscopy Society, CNRS Silver Medallist in 1983 and is a Fellow of the Optical Society of America and of the Microscopy Society of America (Distinguished Scientist, Physics, 2015), Fellow of the Royal Microscopical Society and Honorary Member of the French Microscopy Society. In 1982, he was awarded the ScD degree by the University of Cambridge. In 1982, he took over editorship of the Advances in Electronics & Electron Physics (now Advances in Imaging & Electron Physics) from Claire Marton (widow of the first editor, Bill Marton) and followed Marton's example in maintaining a wide range of subject matter. He added mathematical morphology to the topics regularly covered; Jean Serra and Gerhard Ritter are among those who have contributed. In 1980, he joined Professor Wollnik (Giessen University) and Karl Brown (SLAC) in organising the first international conference on charged-particle optics, designed to bring together opticians from the worlds of electron optics, accelerator optics and spectrometer optics. This was so successful that similar meetings have been held at four-year intervals from 1986 to the present day. Peter Hawkes organised the 1990 meeting in Toulouse and has been a member of the organising committee of all the meetings. He has also partic

Affiliations and Expertise

Laboratoire d'Optique Electronique du Centre National de la Recherche Scientifique (CEMES), Toulouse, France