Advances in Imaging and Electron Physics

Advances in Imaging and Electron Physics

Calculus of Finite Differences in Quantum Electrodynamics

1st Edition - November 25, 2003

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  • Editor: Peter Hawkes
  • eBook ISBN: 9780080490083

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Description

Among the subjects reviewed in these Advances, the properties and computation of electromagnetic fields have been considered on several occasions. In particular, the early work of H.F. Harmuth on Maxwell's equations, which was highly controversial at the time, formed a supplement to the series. This volume, unlike previous volumes in the series concentrates solely on the research of professors' Harmuth and Meffert. These studies raise important and fundamental questions concerning some of the basic areas of physics: electromagnetic theory and quantum mechanics. They deserve careful study and reflection for although the authors do not attempt to provide the definitive answer to the questions, their work is undoubtedly a major step towards such an answer. This volume essential reading for those researchers and academics working applied mathematicians or theoretical physics

Key Features

  • Unlike previous volumes, this book concentrates solely on the new research of professors Harmuth and Meffert
  • Raises important and fundamental questions concerning electromagnetism theory and quantum mechanics
  • Provides the steps in finding answers for the highly debated questions

Readership

Researchers, academics, physicists and engineers working in the field of image and electron physics or applied mathematicians

Table of Contents

    • Preface
    • Future contributions
    • Dedication
    • Foreword
    • List of Frequently used symbols
    • 1: Introduction
      • 1.1 MODIFIED MAXWELL EQUATIONS
      • 1.2 SUMMARY OF RESULTS IN CLASSICAL PHYSICS
      • 1.3 BASIC RELATIONS FOR QUANTUM MECHANICS
      • 1.4 DIPOLE CURRENTS
      • 1.5 INFINITESIMAL AND FINITE DIFFERENCES FOR SPACE AND TIME
    • 2: Differential Equations for the Pure Radiation Field
      • 2.1 PURE RADIATION FIELD
      • 2.2 DIFFERENTIAL SOLUTION FOR w(ζ, θ)
      • 2.3 HAMILTON FUNCTION FOR PLANAR WAVE
      • 2.4 QUANTIZATION OF THE DIFFERENTIAL SOLUTION
      • 2.5 COMPUTER PLOTS FOR THE DIFFERENTIAL THEORY
    • 3: Difference Equations for the Pure Radiation Field
      • 3.1 Basic Difference Equations
      • 3.2 Time Dependent Solution of Ve(ζ, θ)
      • 3.3 Solution for Aev(ζ, θ)
      • 3.4 Magnetic Potential Amv(ζ, θ)
      • 3.5 HAMILTON FUNCTION FOR FINITE DIFFERENCES
      • 3.6 QUANTIZATION OF THE DIFFERENCE SOLUTION
      • 3.7 COMPUTER PLOTS FOR THE DIFFERENCE THEORY
    • 4: Differential Equation for the Klein-Gordon Field
      • 4.1 KLEIN-GORDON EQUATION WITH MAGNETIC CURRENT DENSITY
      • 4.2 STEP FUNCTION EXCITATION
      • 4.3 EXPONENTIAL RAMP FUNCTION EXCITATION
      • 4.4 HAMILTON FUNCTION AND QUANTIZATION
      • 4.5 PLOTS FOR THE DIFFERENTIAL THEORY
    • 5: Difference Equation for the Klein-Gordon Field
      • 5.1 KLEIN-GORDON DIFFERENCE EQUATION
      • 5.2 TIME DEPENDENT SOLUTION OF Ψ(ζ, θ)
      • 5.3 EXPONENTIAL RAMP FUNCTION AS BOUNDARY CONDITION
      • 5.4 HAMILTON FUNCTION FOR DIFFERENCE EQUATION
      • 5.5 PLOTS FOR THE DIFFERENCE THEORY
    • 6: Appendix
      • 6.1 CALCULATIONS FOR SECTION 2.2
      • 6.2 INHOMOGENEOUS DIFFERENCE WAVE EQAUATION
      • 6.3 DIFFERENTIAL DERIVATION OF Aev(ζ,θ)
      • 6.4 CALCULATIONS FOR SECTION 3.3
      • 6.5 CALCULATIONS FOR SECTION 3.4
      • 6.6 CALCULATIONS FOR SECTION 3.5
      • 6.7 CALCULATIONS FOR SECTION 4.4
      • 6.8 CALCULATIONS FOR SECTION 5.4
    • References and Bibliography
    • Index

Product details

  • No. of pages: 312
  • Language: English
  • Copyright: © Academic Press 2003
  • Published: November 25, 2003
  • Imprint: Academic Press
  • eBook ISBN: 9780080490083

About the Series Editor

Peter Hawkes

Peter Hawkes
Peter Hawkes obtained his M.A. and Ph.D (and later, Sc.D.) from the University of Cambridge, where he subsequently held Fellowships of Peterhouse and of Churchill College. From 1959 – 1975, he worked in the electron microscope section of the Cavendish Laboratory in Cambridge, after which he joined the CNRS Laboratory of Electron Optics in Toulouse, of which he was Director in 1987. He was Founder-President of the European Microscopy Society and is a Fellow of the Microscopy and Optical Societies of America. He is a member of the editorial boards of several microscopy journals and serial editor of Advances in Electron Optics.

Affiliations and Expertise

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

About the Authors

Beate Meffert

Affiliations and Expertise

Humboldt University, Berlin, Germany

Henning Harmuth

Affiliations and Expertise

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

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