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UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS Guest
2024-11-22 1:46 |
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Conference: Bucharest University Faculty of Physics 2012 Meeting
Section: Theoretical Physics and Applied Mathematics
Title:
Finite Gaussians and some of their properties
Authors:
N. COTFAS
Affiliation:
Department of Theoretical Physics, Mathematics, Optics, Plasma, Lasers, Faculty of Physics, University of Bucharest
E-mail
ncotfas@yahoo.com
Keywords:
Finite Fourier transform, discrete Wigner function, finite quantum systems
Abstract:
The continuous Gaussians play a fundamental role in physics due to their remarkable properties. By using a Weil-Zak type transform we obtain a finite version of the Gaussian function useful in the case of quantum systems with finite-dimensional Hilbert space. Our finite Gaussians are very similar to the continuous ones. For example, the finite Fourier transform of a finite Gaussian is a finite Gaussian, and the discrete Wigner function corresponding to a finite Gaussian is a sum
of four products of finite Gaussians.
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