Author | Sommerfeld, Arnold. author |
---|---|

Title | Mathematical Theory of Diffraction [electronic resource] / by Arnold Sommerfeld |

Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 2004 |

Connect to | http://dx.doi.org/10.1007/978-0-8176-8196-8 |

Descript | IX, 157 p. online resource |

SUMMARY

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 Poincarรฉ 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

CONTENT

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 -- Translatorsโ{128}{153} 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

Mathematics
Applied mathematics
Engineering mathematics
History
Physics
Optics
Electrodynamics
Optoelectronics
Plasmons (Physics)
Mathematics
Applications of Mathematics
History of Mathematical Sciences
Mathematical Methods in Physics
Optics and Electrodynamics
Optics Optoelectronics Plasmonics and Optical Devices