The discrete harmonic oscillator, Harper's equation, and the discrete fractional Fourier transform
Journal of Physics A: Mathematical and General
Institute of Physics Publishing
2209 - 2222
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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.