Wave-Particle Complementarity and Reciprocity of Gauss Sums on Talbot Effects

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Berry and Klein (J. Mod. Opt. (1997) 43 2139-2164) showed that the Talbot effects in classical optics are naturally explained by Gauss sums studied in number theory. Their result was based on Helmholtz equation. In this article, we explain the effect based on Fresnel integral also by Gauss sums. These two explanations are shown to agree with by the reciprocity law of Gauss sums. The relation between this agreement and the wave-particle complementarity is also discussed.
AMS-TeX, 14 pages

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Mathematical Physics, Number Theory

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http://salesiana.dossiersoluciones.com/handle/123456789/57101

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math-ph/0207011
 http://arxiv.org/abs/math-ph/0207011

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arXiv