The Mathematics of Superoscillations

Released on by Yakir Aharonov
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  • The Mathematics of Superoscillations Book Detail

  • Author : Yakir Aharonov
  • Release Date : 2017-04-25
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 120
  • ISBN 13 : 1470423243
  • File Size : 20,20 MB
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The Mathematics of Superoscillations by Yakir Aharonov PDF Summary

Book Description: In the past 50 years, quantum physicists have discovered, and experimentally demonstrated, a phenomenon which they termed superoscillations. Aharonov and his collaborators showed that superoscillations naturally arise when dealing with weak values, a notion that provides a fundamentally different way to regard measurements in quantum physics. From a mathematical point of view, superoscillating functions are a superposition of small Fourier components with a bounded Fourier spectrum, which result, when appropriately summed, in a shift that can be arbitrarily large, and well outside the spectrum. The purpose of this work is twofold: on one hand the authors provide a self-contained survey of the existing literature, in order to offer a systematic mathematical approach to superoscillations; on the other hand, they obtain some new and unexpected results, by showing that superoscillating sequences can be seen of as solutions to a large class of convolution equations and can therefore be treated within the theory of analytically uniform spaces. In particular, the authors will also discuss the persistence of the superoscillatory behavior when superoscillating sequences are taken as initial values of the Schrödinger equation and other equations.

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The Mathematics of Superoscillations

The Mathematics of Superoscillations

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In the past 50 years, quantum physicists have discovered, and experimentally demonstrated, a phenomenon which they termed superoscillations. Aharonov and his co

Advanced Mathematical Methods

Advanced Mathematical Methods

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This text is a self-contained second course on mathematical methods dealing with topics in linear algebra and multivariate calculus that can be applied to stati