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

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

68 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

Access to Document

10.1088/0305-4470/33/11/304

Cite this

@article{e63089d9b686418a828dc1c877765e61,

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.",

author = "Laurence Barker and {\c C}aǧatay Candan and Tuǧrul Hakioǧlu and Kutay, {M. Alper} and Ozaktas, {Haldun M.}",

year = "2000",

month = mar,

day = "24",

doi = "10.1088/0305-4470/33/11/304",

language = "English",

volume = "33",

pages = "2209--2222",

journal = "Journal of Physics A: Mathematical and General",

issn = "0305-4470",

publisher = "IOP Publishing Ltd.",

number = "11",

}

TY - JOUR

T1 - The discrete harmonic oscillator, Harper's equation, and the discrete fractional Fourier transform

AU - Barker, Laurence

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.

UR - http://www.scopus.com/inward/record.url?scp=0034708297&partnerID=8YFLogxK

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

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

M3 - Article

AN - SCOPUS:0034708297

SN - 0305-4470

VL - 33

SP - 2209

EP - 2222

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

IS - 11

ER -

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

Abstract

Access to Document

Other files and links

Fingerprint

Cite this