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