Skip to main content

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 . 065028: 1-14. 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)

PDF - Publisher pdf
Restricted to Repository staff only
Contact us about this Publication Download (965kB)
[img]
Official URL
http://dx.doi.org/10.1088/0143-0807/36/6/065028

Abstract

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: Faculties > Sciences > School of Physical Sciences
Depositing User: Paul Strange
Date Deposited: 02 Oct 2015 16:26 UTC
Last Modified: 17 Jul 2019 10:41 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/50755 (The current URI for this page, for reference purposes)
  • Depositors only (login required):

Downloads

Downloads per month over past year