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© 2017

Green’s Functions in Classical Physics

  • Demonstrates how the Green’s functions approach can be useful in a variety of fields of classical physics

  • Provides an overview of classical physics and a short outlook on quantum mechanics from a consistent Green’s function point of view

  • Concerns not only methodical and mathematical aspects of solving partial differential equations of physics, but also conceptual and epistemological aspects in physics in general

  • Demonstrates that some aspects discussed so far only in modern physics (quantum mechanics, quantum statistics, etc.) can be transferred with benefit also to the physics of classical particles and fields

Book

Part of the Lecture Notes in Physics book series (LNP, volume 938)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Tom Rother
    Pages 1-13
  3. Tom Rother
    Pages 95-147
  4. Tom Rother
    Pages 235-251
  5. Back Matter
    Pages 253-267

About this book

Introduction

This book presents the Green’s function formalism in a basic way and demonstrates its usefulness for applications to several well-known problems in classical physics which are usually solved not by this formalism but other approaches. The book bridges the gap between applications of the Green’s function formalism in quantum physics and classical physics. This book is written as an introduction for graduate students and researchers who want to become more familiar with the Green’s function formalism.

In 1828 George Green has published an essay that was unfortunately sunken into oblivion shortly after its publication. It was rediscovered only after several years by the later Lord Kelvin. But since this time, using Green’s functions for solving partial differential equations in physics has become an important mathematical tool. While the conceptual and epistemological importance of these functions were essentially discovered and discussed in modern physics - especially in quantum field theory and quantum statistics - these aspects are rarely touched in classical physics. In doing it, this book provides an interesting and sometimes new point of view on several aspects and problems in classical physics, like the Kepler motion or the description of certain classical probability experiments in finite event spaces. A short outlook on quantum mechanical problems concludes this book.

Keywords

Solution of Partial Differential Equations in Physics Green’s function formalism Principle of Causality Principle of Reciprocity Scattering Effects Probability Experiments Double-Slit Experiment Kepler Motion

Authors and affiliations

  1. 1.German Aerospace Center NeustrelitzGermany

About the authors

Dr. Tom Rother was born in 1957 in Wolfen, Germany. He received the Dr. rer. nat. and Dr. habil. degrees from the University of Greifswald in 1987 and 1999. Since 1987, he has been with the German Aerospace Center. In 1990, he received the Young Scientist Scholarship of the URSI, and in 1991 a special grant of the Alexander von Humboldt Foundation. He is a Senior Scientist of the German Aerospace Center since 2004. Dr. Rother’s research interests are in quantum statistics of charged particle systems, in electromagnetic wave theory, and in quantum optics. With Springer he has published 2 books on electromagnetic wave scattering on nonspherical particles.

Bibliographic information

Industry Sectors
Energy, Utilities & Environment

Reviews

“This book serves as a valuable and self-contained introduction for those who want to become more familiar with GFs and their importance and usage in classical physics” (Nikolaos L. Tsitsas, Mathematical Reviews, June, 2018)