Sommerfeld Mathematical Theory of Diffraction

Erscheinungsjahr 2012
ISBN: 978-0-8176-8196-8
Verlag: Birkhäuser Boston
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 35, 157 Seiten, eBook

Reihe: Progress in Mathematical Physics

Arnold Sommerfeld's "Mathematische Theorie der Diffraction" marks a milestone in optical theory, full of insights that are still relevant today. In a stunning tour de force, Sommerfeld derives the first mathematically rigorous solution of an optical diffraction problem. Indeed, his diffraction analysis is a surprisingly rich and complex mix of pure and applied mathematics, and his often-cited diffraction solution is presented only as an application of a much more general set of mathematical results. The body of Sommerfeld's work is devoted to the systematic development of a method for deriving solutions of the wave equation on Riemann surfaces, a fascinating but perhaps underappreciated topic in mathematical physics.

Zielgruppe

Research

Autoren/Hrsg.

Sommerfeld, Arnold

Weitere Mitwirkende

Nagem, Raymond J.

Zampolli, Mario

Sandri, Guido

Inhaltsverzeichnis

Mathematical Theory of Diffraction.- 1. General problem formulation.- 2. Expansions in Bessel functions.- 3. Transition from ?u = 0 to ?u + k2u = 0.- 4. Bessel functions as the simplest examples.- 5. Everywhere finite solutions.- 6. Solutions with a singularity.- 7. Graphical treatment of the simplest multivalued solution.- 8. Application to diffraction.- Tafel.- Translators’ Notes.- References.- Appendix I: The History and Present State of Discoveries relating to Vision, Light and Colours.- Appendix II: On the Mathematical Theory of Diffraction Phenomena.