The discrete harmonic oscillator, Harper's equation, and the discrete fractional Fourier transform


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BARKER L., Candan C. , HAKIOGLU T., KUTAY M., OZAKTAS H.

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, vol.33, no.11, pp.2209-2222, 2000 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 33 Issue: 11
  • Publication Date: 2000
  • Doi Number: 10.1088/0305-4470/33/11/304
  • Title of Journal : JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
  • Page Numbers: pp.2209-2222

Abstract

Certain solutions to Harper's equation are discrete analogues of (and approximations to) the Hermite-Gaussian functions. They are the energy eigenfunctions of a-discrete algebraic analogue of the harmonic oscillator, and they lead to a definition of a discrete fractional Fourier transform (FT). The discrete fractional FT is essentially the time-evolution operator of the discrete harmonic oscillator.