The discrete harmonic oscillator, Harper's equation, and the discrete fractional Fourier transform
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, vol.33, no.11, pp.2209-2222, 2000 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 33 Issue: 11
- Publication Date: 2000
- Doi Number: 10.1088/0305-4470/33/11/304
- Journal Name: JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.2209-2222
- Open Archive Collection: AVESIS Open Access Collection
- Middle East Technical University Affiliated: Yes
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.