Wave Phenomena and Classical Electrodynamics Without Calculations

Part of the Lecture Notes in Physics book series (LNP, volume 747)

Let us consider the well-known problem of diffraction of an initially plane wave with wave vector k on a round hole of radius a in a thin screen. If the radius of the hole is sufficiently large, so that ka ≫ 1, then the wave remains essentially plane after going through the hole, with a small distortion due to a diffraction on the edges of the hole. Now we start diminishing a. The wave gets more and more distorted after going through the hole. Indeed, the allowed transverse component of the wave vector in it increases in accordance with the uncertainty relation Δkta ≳ 1. At last, with a ∼ 1/k (or a ∼ λ, where λ is the wavelength) the outgoing wave becomes spherical, since in this case the transverse component of the wave vector in it kt ≳ 1/a reaches its maximum allowed value k.


Wave Vector Wave Packet Uncertainty Relation Time Reversal Electric Dipole Moment 
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  1. Curiously, its resolution, at least in the classical version of the problem, does not create usually great difficulties for qualified experimentalists. On the other hand, this question sometimes turns out very difficult for quite well-known theorists.Google Scholar
  2. Let us note that just the δ-function term in this expression is responsible for the hyperfine splitting of s-levels in atoms and ions caused by the nuclear magnetic moment.Google Scholar
  3. See, for instance: L.D. Landau and E.M. Lifshitz, The Classical Theory of Fields . §74.Google Scholar
  4. In the discussion of this problem we essentially follow R. Hagedorn (1966).Google Scholar
  5. The presentation here follows a paper by A. D. Dolgov, I. B. Khriplovich (1981).Google Scholar

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