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# Advances in Imaging and Electron Physics

## Calculus of Finite Differences in Quantum Electrodynamics

- 1st Edition, Volume 129 - November 25, 2003
- Authors: Beate Meffert, Henning Harmuth
- Editor: Peter W. Hawkes
- Language: English
- Hardback ISBN:9 7 8 - 0 - 1 2 - 0 1 4 7 7 1 - 7
- Paperback ISBN:9 7 8 - 0 - 1 2 - 3 8 8 5 2 0 - 3
- eBook ISBN:9 7 8 - 0 - 0 8 - 0 4 9 0 0 8 - 3

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… Read more

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Request a sales quoteAmong 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

- 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

- 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 V
_{e}(ζ, θ) - 3.3 Solution for A
_{ev}(ζ, θ) - 3.4 Magnetic Potential A
_{mv}(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 A
_{ev}(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

- No. of pages: 312
- Language: English
- Edition: 1
- Volume: 129
- Published: November 25, 2003
- Imprint: Academic Press
- Hardback ISBN: 9780120147717
- Paperback ISBN: 9780123885203
- eBook ISBN: 9780080490083

PH

### Peter W. Hawkes

BM

### Beate Meffert

HH

### Henning Harmuth

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