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

Download

index.pdf

Date

2000-03-24

Author

BARKER, L
Candan, Çağatay
HAKIOGLU, T
KUTAY, MA
OZAKTAS, HM

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

211
views

0
downloads

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

Suggestions

OpenMETU
Core

The path integral quantization and the construction of the S-matrix operator in the Abelian and non-Abelian Chern-Simons theories Fainberg, VY; Pak, Namık Kemal; Shikakhwa, MS (IOP Publishing, 1997-06-07) The covariant path integral quantization of the theory of the scalar and spinor fields interacting through the Abelian and non-Abelian Chern-Simons gauge fields in 2 + 1 dimensions is carried out using the De Witt-Fadeev-Popov method. The mathematical ill-definiteness of the path integral of theories with pure Chern-Simons' fields is remedied by the introduction of the Maxwell or Maxwell-type (in the non-Abelian case) terms, which make the resulting theories super-renormalizable and guarantees their gauge-i...
A new integrable generalization of the Korteweg-de Vries equation Karasu-Kalkanli, Ayse; Karasu, Atalay; Sakovich, Anton; Sakovich, Sergei; TURHAN, REFİK (AIP Publishing, 2008-07-01) A new integrable sixth-order nonlinear wave equation is discovered by means of the Painleve analysis, which is equivalent to the Korteweg-de Vries equation with a source. A Lax representation and an auto-Backlund transformation are found for the new equation, and its traveling wave solutions and generalized symmetries are studied. (C) 2008 American Institute of Physics.
Finite action Yang-Mills solutions on the group manifold Dereli, T; Schray, J; Tucker, RW (IOP Publishing, 1996-08-21) We demonstrate that the left (and right) invariant Maurer-Cartan forms for any semi-simple Lie group enable solutions of the Yang-Mills equations to be constructed on the group manifold equipped with the natural Cartan-Killing metric. For the unitary unimodular groups the Yang-Mills action integral is finite for such solutions. This is explicitly exhibited for the case of SU(3).
The Lie algebra sl(2,R) and so-called Kepler-Ermakov systems Leach, PGL; Karasu, Emine Ayşe (Informa UK Limited, 2004-05-01) A recent paper by Karasu (Kalkanli) and Yildirim (Journal of Nonlinear Mathematical Physics 9 (2002) 475-482) presented a study of the Kepler-Ermakov system in the context of determining the form of an arbitrary function in the system which was compatible with the presence of the sl(2, R) algebra characteristic of Ermakov systems and the existence of a Lagrangian for a subset of the systems. We supplement that analysis by correcting some results.
Systematical approach to the exact solution of the Dirac equation for a deformed form of the Woods-Saxon potential Berkdemir, Cueneyt; Berkdemir, Ayse; Sever, Ramazan (IOP Publishing, 2006-10-27) The exact solution of the Dirac equation for a deformed form of the Woods Saxon potential is obtained for the s-wave relativistic energy spectrum. The energy eigenvalues and two-component spinor wavefunctions are derived analytically by using a systematical method which is called Nikiforov - Uvarov. It is seen that the energy eigenvalues and the wavefunctions strongly depend on the parameters of the potential. In addition, it is also shown that the non-relativistic limit can be reached easily and directly f...

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.