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Evolution of superoscillations in the quantum mechanical harmonic oscillator

Bussell, Max, Strange, Paul (2015) Evolution of superoscillations in the quantum mechanical harmonic oscillator. European Journal of Physics, 36 . ISSN 0143-0807. (doi:10.1088/0143-0807/36/6/065028) (Access to this publication is currently restricted. You may be able to access a copy if URLs are provided) (KAR id:50755)

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A superoscillatory function is one in which the function oscillates faster than its fastest Fourier component. Superoscillations are now a well-established feature of certain types of wavepacket. Here we discuss quantum superoscillations in a wavepacket evolving according to the harmonic oscillator hamiltonian. The evolution of the wavepacket is investigated using an expansion in terms of eigenfunctions and in terms of the propagator using both

an exact integration, and a saddle point approximation. The creation and decay of superoscillations as well as the barrier between them and normal oscillations is shown to depend on the behaviour of the saddle points. The work reported here is the result of a student project and we argue that super oscillations makes an excellent topic with which to introduce students to theoretical research.

Item Type: Article
DOI/Identification number: 10.1088/0143-0807/36/6/065028
Uncontrolled keywords: Physics of Quantum Materials
Subjects: Q Science > QC Physics > QC174.12 Quantum theory
Divisions: Divisions > Division of Natural Sciences > Physics and Astronomy
Depositing User: Paul Strange
Date Deposited: 02 Oct 2015 16:26 UTC
Last Modified: 17 Aug 2022 10:59 UTC
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