Barker, L.Candan, C.Hakioğlu, T.Kutay, M. A.Özaktaş, Haldun M.2016-02-082016-02-0820000305-4470http://hdl.handle.net/11693/25066Certain 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.EnglishArticle10.1088/0305-4470/33/11/304