The Mathematics of Superoscillations

The Mathematics of Superoscillations
Author :
Publisher : American Mathematical Soc.
Total Pages : 120
Release :
ISBN-10 : 9781470423247
ISBN-13 : 1470423243
Rating : 4/5 (243 Downloads)

Book Synopsis The Mathematics of Superoscillations by : Yakir Aharonov

Download or read book The Mathematics of Superoscillations written by Yakir Aharonov and published by American Mathematical Soc.. This book was released on 2017-04-25 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


The Mathematics of Superoscillations Related Books

The Mathematics of Superoscillations
Language: en
Pages: 120
Authors: Yakir Aharonov
Categories: Mathematics
Type: BOOK - Published: 2017-04-25 - Publisher: American Mathematical Soc.

GET EBOOK

In the past 50 years, quantum physicists have discovered, and experimentally demonstrated, a phenomenon which they termed superoscillations. Aharonov and his co
A Half-Century of Physical Asymptotics and Other Diversions
Language: en
Pages: 200
Authors: Michael Berry
Categories: Science
Type: BOOK - Published: 2017-07-19 - Publisher: World Scientific

GET EBOOK

Michael Berry is a theoretical physicist who has contributed to a wide variety of areas in quantum mechanics, optics and related mathematics, linked by the geom
Recent Developments in Operator Theory, Mathematical Physics and Complex Analysis
Language: en
Pages: 424
Authors: Daniel Alpay
Categories: Mathematics
Type: BOOK - Published: 2023-04-11 - Publisher: Springer Nature

GET EBOOK

This book features a collection of papers by plenary, semi-plenary and invited contributors at IWOTA2021, held at Chapman University in hybrid format in August
Advanced Mathematical Methods
Language: en
Pages: 564
Authors: Adam Ostaszewski
Categories: Mathematics
Type: BOOK - Published: 1990 - Publisher: Cambridge University Press

GET EBOOK

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
Theoretical Physics, Wavelets, Analysis, Genomics
Language: en
Pages: 650
Authors: Patrick Flandrin
Categories: Mathematics
Type: BOOK - Published: 2023-05-31 - Publisher: Springer Nature

GET EBOOK

Over the course of a scientific career spanning more than fifty years, Alex Grossmann (1930-2019) made many important contributions to a wide range of areas inc