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

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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

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Department of Electrical and Electronics Engineering, Article

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Citation Formats

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, pp. 2209–2222, 2000, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/37930.