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

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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.

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Journal of Physics A: Mathematical and General

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Institute of Physics Publishing

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Published Version (Please cite this version)

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English