Title
On some quantum and analytical properties of fractional Fourier transforms
Abstract
Fractional Fourier transforms (FrFT) are a natural one-parameter family of unitary transforms that have the ordinary Fourier transform embedded as a special case. In this paper, following the efforts of several authors, we explore the theory and applications of FrFT, from the standpoints of both quantum mechanics and analysis. These include the phase plane interpretation of FrFT, FrFT's role in the order reduction of certain classes of differential equations, the integral representation of FrFT, and its Paley-Wiener theorem and Heisenberg uncertainty principle. Our two major tools are quantum operator algebra and asymptotic analysis such as the singular perturbation theory and the stationary phase technique.
Related to
Institute for Mathematics and Its Applications>IMA Preprints Series
Suggested Citation
Shen, Jianhong.
(2002).
On some quantum and analytical properties of fractional Fourier transforms.
Retrieved from the University of Minnesota Digital Conservancy,
https://hdl.handle.net/11299/3772.