Green’s Functions in Classical Physics

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.

“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)

• Prologue.- About the State of Physics.- Basic Structural Elements of Physics.- About Classical Physics and Quantum Mechanics.- Green's Functions of Classical Particles.- The Simple Harmonic Oscillator.- The Damped Harmonic Oscillator.- Elementary Motions of a Point Mass.- Lippmann-Schwinger Equation.- Two Systematic Ways to Derive Green's Functions.- Temporal Boundary Value Problem of the Harmonic Oscillator.- Two Simple Interaction Processes and Huygens' Principle.- Particle Scattering on a Rigid Sphere and Kepler Problem.- Green's Functions of Classical Fields.- Comments on the Field Concept.- The Elastic String.- Poisson Equations of Higher Dimensions.- Wave Equations of Higher Dimensions.- The Scalar Helmholtz Equation.- Scattering Problems.- Probability Experiments and Green's Functions in Classical Event Spaces.- Probability Experiments in a Two-Dimensional Event Space.- Probability Experiments in a Four-Dimensional Event Space.- Outlook or Something Like an End.- Classical Free Point Mass and Green's Function of the Diffusion Equation.- Schrödinger Equation of the Free Particle and Green's Function.- Classical Fokker-Planck Equation and Schrödinger Equation.- A Relation Between the Green's Functions of the Klein-Gordon- and Dirac Equation.