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

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dc.creatorMatsutani, Shigeki
dc.creatorÔnishi, Yoshihiro
dc.date2002-07-07
dc.date.accessioned2026-07-07T04:29:18Z
dc.date.available2026-07-07T04:29:18Z
dc.descriptionBerry 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.
dc.descriptionAMS-TeX, 14 pages
dc.identifierhttps://arxiv.org/abs/math-ph/0207011
dc.identifierhttp://arxiv.org/abs/math-ph/0207011
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57101
dc.subjectMathematical Physics
dc.subjectNumber Theory
dc.titleWave-Particle Complementarity and Reciprocity of Gauss Sums on Talbot Effects
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