Mathematical Theory of Diffraction
By: by Arnold Sommerfeld
Series: Progress in Mathematical Physics -- 35; Progress in mathematical physics -- 35.
Publisher: Birkhäuser Boston; Imprint: Birkhäuser
Published: 2004
Place of publication: Boston, MA
Language: eng
Format: [electronic resource] /
Number of pages: 157
ISBN-13: 9781461264859; 9780817681968
Subjects: Mathematics; Mathematical physics
Description: Arnold Sommerfeld's Mathematical Theory of 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. This complete translation, reflecting substantial scholarship, is the first publication in English of Sommerfeld's original work. The extensive notes by the translators are rich in historical background and provide many technical details for the reader. A detailed account of the previous diffraction analyses of Kirchhoff and Poincaré provides a context for the striking originality and power of Sommerfeld's ideas. The availability of this translation is an enriching contribution to the community of mathematical and theoretical physicists.
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Table of contents: title: Preface; title: Introduction; title: Mathematical Theory of Diffraction; title: General problem formulation; title: Expansions in Bessel functions; title: Transition formula; title: Bessel functions as the simplest examples; title: Everywhere finite solutions; title: Solutions with a singularity; title: Graphical treatment of the simplest multivalued solution; title: Application to diffraction; title: Tafel; title: Translators' Notes; title: Appendix I: The History and Present State of Discoveries relating to Vision, Light and Colours, Joseph Priestley, London, 1772, pp. 171-182; title: Index.