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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.
List of contents
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.
About the author
Dr. Robert Brehm
Studium in Frankfurt, bis 1974 wissenschaftlicher Mitarbeiter
an der Universität Frankfurt, Promotion über ein öffentlichrechtliches
Thema, seit 1975 Rechtsanwalt in Frankfurt-Sindlingen. Autor verschiedener
Fachveröffentlichungen im öffentlichen Recht, insbesondere
im Hochschulzulassungs- und Prüfungsrecht, derzeit an der
Vorbereitung eines Prüfungsrechtsbuchs zusammen mit zwei
Verwaltungsrichtern.
Dr. Alfred W. Breinersdorfer
Studium der Rechtswissenschaft und Soziologie in Tübingen,
Promotion über Gleichheit der Bildungschancen, vorübergehende
Tätigkeit im Rechts- und Planungsteam der Universität
Tübingen und wissenschaftlicher Mitarbeiter bei der Juristischen
Fakultät. Autor zahlreicher Publikationen im Hochschulrecht,
seit 1976 Rechtsanwalt in Stuttgart, Fachanwalt für Verwaltungsrecht.
Dr. Wolfgang Zimmerling
rechtswissenschaftliches Studium an der Universität des Saarlandes,
sodann Assistent an der Universität. Promotion über
ein hochschulrechtliches Thema. Seit 1977 als Rechtsanwalt in
Saarbrücken zugelassen, Fachanwalt für Verwaltungsrecht
sowie Fachanwalt für Arbeitsrecht, Autor zahlreicher hochschul-
und arbeitsrechtlicher Veröffentlichungen. Ständiger
Rechtsberater der Studierendenschaft der Universität des
Saarlandes.
Die Autoren haben sich am 1. Januar 1990 zur ersten überörtlichen
Sozietät auf dem Gebiet des Verwaltungsrechts zusammengeschlossen,
nachdem sie bereits mehr als 10 Jahre auf dem Gebiet des Hochschulzulassungsrechts,
des Allgemeinen Hochschulrechts und des Prüfungsrechts eng
miteinander kooperiert haben.
Summary
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.
Additional text
From the reviews:
“This is a very nice book for those interested in the theory of diffraction since it presents, for the first time in English, the strikingly original work of Sommerfeld—which marks a milestone in optical theory—enriched with historical background and technical details. The interest of this book is not only historical but also technical as it presents a surprisingly rich and complex mix of pure and applied mathematics.”(MATHEMATICAL REVIEWS)
"This book offers the first publication in English of Sommerfeld’s original work, together with extensive notes by the translators, and it can be recommended to anyone interested in the theory of diffraction. … The translator’s notes (64 pages) are very illuminating for the reader by providing a lot of historical remarks, technical details, and a nice account of previous diffraction analyses of Kirchhoff and Poincaré." (Johannes Elschner, Zentralblatt MATH, Vol. 1109 (11), 2007)
Report
From the reviews:
"This is a very nice book for those interested in the theory of diffraction since it presents, for the first time in English, the strikingly original work of Sommerfeld-which marks a milestone in optical theory-enriched with historical background and technical details. The interest of this book is not only historical but also technical as it presents a surprisingly rich and complex mix of pure and applied mathematics."(MATHEMATICAL REVIEWS)
"This book offers the first publication in English of Sommerfeld's original work, together with extensive notes by the translators, and it can be recommended to anyone interested in the theory of diffraction. ... The translator's notes (64 pages) are very illuminating for the reader by providing a lot of historical remarks, technical details, and a nice account of previous diffraction analyses of Kirchhoff and Poincaré." (Johannes Elschner, Zentralblatt MATH, Vol. 1109 (11), 2007)
