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The discrete harmonic oscillator, Harper's equation, and the discrete fractional Fourier transform
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Date
2000-03-24
Author
BARKER, L
Candan, Çağatay
HAKIOGLU, T
KUTAY, MA
OZAKTAS, HM
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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.
Subject Keywords
Mathematical Physics
,
General Physics and Astronomy
,
Statistical and Nonlinear Physics
URI
https://hdl.handle.net/11511/37930
Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
DOI
https://doi.org/10.1088/0305-4470/33/11/304
Collections
Department of Electrical and Electronics Engineering, Article
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BibTeX
L. BARKER, Ç. Candan, T. HAKIOGLU, M. KUTAY, and H. OZAKTAS, “The discrete harmonic oscillator, Harper’s equation, and the discrete fractional Fourier transform,”
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
, vol. 33, no. 11, pp. 2209–2222, 2000, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/37930.