Elsevier S & T

Advances in Imaging and Electron Physics: Dogma of the Continuum and the Calculus of Finite Differences in Quantum Physics

Meffert, Beate; Harmuth, Henning

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Table of contents
  • Contentsv
  • Prefaceix
  • Future Contributionsxi
  • Dedicationxvii
  • Forewordxix
  • List of Frequently Used Symbolsxxiii
  • Chapter 1. Introduction1
  • 1.1 Modified Maxwell Equations and Basic Relations1
  • 1.2 Basic Concepts of the Calculus of Finite Differences8
  • 1.3 Lagrange Function and Modified Maxwell Equations18
  • 1.4 Dogma of the Continuum in Physics26
  • 1.5 Concept of Space Based on Finite Differences30
  • Chapter 2. Modified Klein-Gordon Equation44
  • 2.1 Differential Equation with Magnetic Current Density44
  • 2.2 Modified Klein-Gordon Difference Equation52
  • 2.3 Solution of the Difference Equation of Ψx061
  • 2.4 Time-Dependent Solution of Ψx0(ζ, θ)70
  • 2.5 Hamilton Function and Quantization78
  • 2.6 Plots for First-Order Approximation86
  • Chapter 3. Inhomogeneous Difference Equation92
  • 3.1 Inhomogeneous Term of Eq. (2.2-31)92
  • 3.2 Evaluation of Eq. (3.1-32)102
  • 3.3 Quantization of the Solution for Δx >> h/m0c115
  • 3.4 Evaluation of the Energy Ûc122
  • 3.5 Plots for Second-Order Approximation135
  • Chapter 4. Klein-Gordon Difference Equation for Small Distances143
  • 4.1 Evaluation of the Difference Equation for Δx << h/m0c143
  • 4.2 Evaluation of Eq. (4.1-4)147
  • 4.3 Quantization of the Solution for Δx << h/m0c155
  • 4.4 Evaluation of the Energy Ûc for Small Distances163
  • Chapter 5. Difference Equation in Spherical Coordinates183
  • 5.1 Charged Particle in an Electromagnetic (EM) Field183
  • 5.2 Relativistic Mass Variation189
  • 5.3 Quantization with Differential Operators198
  • 5.4 Difference Operators203
  • 5.5 Spatial Difference Equation211
  • 5.6 Quantization of the Solution Ψr0(ρ, θ)222
  • 5.7 Convergence for Small Values of Δr226
  • 5.8 Plots for Sections 5.5 and 5.7230
  • 5.9 Origin of the Coulomb Field243
  • 5.10 Unbounded Bosons in a Coulomb Field244
  • 5.11 Antiparticles257
  • Chapter 6. Appendix262
  • 6.1 Difference Operators of Higher Order262
  • 6.2 Extension of Section 3.1 for Δx << λc266
  • 6.3 Solution of Inhomogeneous Difference Equations268
  • 6.4 Calculations for Section 4.2278
  • 6.5 Formulas for Spherical Coordinates284
  • 6.6 Difference Equations Solved by Polynomials288
  • 6.7 Discrete Spherical Harmonics293
  • 6.8 Solution of the Differential Equation (5.5-12)298
  • 6.9 Conformal Mapping for Section 5.7300
  • 6.10 Conformal Mapping for Section 5.10311
  • References and Bibliography314
  • Index318
Book details
  • Vendor Elsevier S & T
  • SKU 9780120147793
  • ISBN-13 9780080526249
  • Author Meffert, Beate; Harmuth, Henning
  • Category Science
  • Subject Electron Microscopes & Microscopy

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Advances in Imaging and Electron Physics merges two long-running serials-Advances in Electronics and Electron Physics and Advances in Optical and Electron Microscopy. This series features extended articles on the physics of electron devices (especially semiconductor devices), particle optics at high and low energies, microlithography, image science and digital image processing, electromagnetic wave propagation, electron microscopy, and the computing methods used in all these domains.