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

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Department of Electrical and Electronics Engineering, Article

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, vol. 33, no. 11, pp. 2209–2222, 2000, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/37930.