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When a beam of light impinges on a structure with spatial periodicity, such as a crystal or a standing wave of light, William Duane hypothesized〔 that there occurs ''transfer in quanta of momentum'', which is observed as diffraction or scattering of the beam. On the discovery of diffraction of particles such as electrons, Duane's principle was seen to cover this case as well.〔Bitsakis, E.(1997). The wave-particle duality, pp. 333–348 in ''The Present Status of the Quantum Theory of Light: Proceedings of a Symposium in Honour of Jean-Pierre Vigier'', edited by Whitney, C.K., Jeffers, S., Roy, S., Vigier, J.-P., Hunter, G., Springer, ISBN 978-94-010-6396-8, (p. 338 ).〕 ==Old quantum theory== In 1905, going beyond Planck's idea of quantum generation of light, Einstein introduced the idea that light could be interpreted as propagating in quanta of energy.〔 Translated in 〕 In 1916 Einstein further considered the light quantum concept, and indicated that it involved not only quantum energy transfer, but also quantum momentum transfer.〔 and a nearly identical version Translated here () and in 〕 In 1925, shortly before the invention of quantum mechanics, Born drew Einstein's attention to the then new idea of "de Broglie's waves". He wrote "It seems to me that a connection of a completely formal kind exists between these and that other mystical explanation of reflection, diffraction and interference using 'spatial' quantisation which Compton and Duane proposed and which has been more closely studied by Epstein and Ehrenfest."〔Born, M. (1925/1971). (Letter of 15 July 1925 ), pp. 84–85 in ''The Born-Einstein Letters'', translated by I. Born, Macmillan, London.〕〔Epstein, P.S., Ehrenfest, P., (1924). (The quantum theory of the Fraunhofer diffraction ), ''Proc. Natl. Acad. Sci.'' 10: 133–139.〕〔Ehrenfest, P., Epstein, P.S. (1924/1927). (Remarks on the quantum theory of diffraction ), ''Proc. Natl. Acad. Sci.'' 13: 400–408.〕 Examining the hypothesis of Duane on quantized momentum transfer, as it accounted for X-ray diffraction by crystals,〔Duane, W. (1923). (The transfer in quanta of radiation momentum to matter, ''Proc. Natl. Acad. Sci.'' 9(5): 158–164 ).〕 and its follow-up by Compton,〔Compton, A.H. (1923). (The quantum integral and diffraction by a crystal, ''Proc. Natl. Acad. Sci.'' 9(11): 360–362 ).〕 Epstein and Ehrenfest had written "The phenomena of Fraunhofer diffraction can be treated as well on the basis of the wave theory of light as by a combination of concept of light quanta with Bohr's principle of correspondence." Using Duane's 1923 hypothesis, the old quantum theory and the de Broglie relation, linking wavelengths and frequencies to energy and momenta, gives an account of diffraction of material particles.〔Heisenberg, W. (1930). (''The Physical Principles of the Quantum Theory'' ), translated by C. Eckart and F.C. Hoyt, University of Chicago Press, Chicago, pp. 77–78.〕〔Pauling, L.C., Wilson, E.B. (1935). ''Introduction to Quantum Mechanics: with Applications to Chemistry'', McGraw-Hill, New York, (pp. 34–36 ).〕〔Landé, A. (1951). (''Quantum Mechanics'' ), Sir Isaac Pitman and Sons, London, pp. 19–22.〕〔Bohm, D. (1951). ''Quantum Theory'', Prentice Hall, New York, pp. 71–73.〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Duane's hypothesis」の詳細全文を読む スポンサード リンク
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