Analysis of Superoscillatory Wave Functions

Details Analysis of Superoscillatory Wave Functions Analysis of Superoscillatory Wave Functions

2004-05-13

arxiv.org/abs/quant-ph/0405065v1

J.Math.Phys. 46 (2005) 012101

Physics

Quantum Physics

20 pages, several figures

Scientific paper

10.1063/1.1825076

Surprisingly, differentiable functions are able to oscillate arbitrarily faster than their highest Fourier component would suggest. The phenomenon is called superoscillation. Recently, a practical method for calculating superoscillatory functions was presented and it was shown that superoscillatory quantum mechanical wave functions should exhibit a number of counter-intuitive physical effects. Following up on this work, we here present more general methods which allow the calculation of superoscillatory wave functions with custom-designed physical properties. We give concrete examples and we prove results about the limits to superoscillatory behavior. We also give a simple and intuitive new explanation for the exponential computational cost of superoscillations.

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