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

Laurence Barker; Çaǧatay Candan; Tuǧrul Hakioǧlu; M. Alper Kutay; Haldun M. Ozaktas

doi:10.1088/0305-4470/33/11/304

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

Laurence Barker^*
, Çaǧatay Candan
, Tuǧrul Hakioǧlu
, M. Alper Kutay
, Haldun M. Ozaktas

^*Corresponding author for this work

Bilkent University
Georgia Institute of Technology

Research output: Contribution to journal › Article › peer-review

69 Citations (Scopus)

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.

Original language	English
Pages (from-to)	2209-2222
Number of pages	14
Journal	Journal of Physics A: Mathematical and General
Volume	33
Issue number	11
DOIs	https://doi.org/10.1088/0305-4470/33/11/304
Publication status	Published - 24 Mar 2000
Externally published	Yes

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Cite this

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

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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AU - Candan, Çaǧatay

AU - Hakioǧlu, Tuǧrul

AU - Kutay, M. Alper

AU - Ozaktas, Haldun M.

PY - 2000/3/24

Y1 - 2000/3/24

N2 - 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.

AB - 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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U2 - 10.1088/0305-4470/33/11/304

DO - 10.1088/0305-4470/33/11/304

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JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

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ER -

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

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