The discrete harmonic oscillator, Harper's equation, and the discrete fractional Fourier transform
- 10 March 2000
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 33 (11) , 2209-2222
- https://doi.org/10.1088/0305-4470/33/11/304
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.Keywords
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