| |
 |
UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS Guest
2024-11-23 18:05 |
 |
|
|
|
Conference: Bucharest University Faculty of Physics 2014 Meeting
Section: Theoretical Physics and Applied Mathematics
Title:
Discrete Wigner function and finite Gaussians
Authors:
N. COTFAS
Affiliation:
Faculty of Physics, University of Bucharest
E-mail
ncotfas@yahoo.com
Keywords:
discrete Wigner function, discrete Fourier transform, Gaussian functions
Abstract:
The Gaussian functions of continuous variable play a fundamental role in quantum physics. The Fourier transform of a Gaussian function is a Gaussian function and the Wigner function corresponding to a Gaussian function is a product of two Gaussian functions. They also have many other remarkable properties. A finite counterpart of Gaussian functions can be defined by using the Jacobi theta function or by directly using certain series. The quantum systems with finite-dimensional Hilbert space are used in Quantum Information and in other applications of quantum physics. It is known that the discrete Fourier transform of a finite Gaussian is a finite Gaussian. We prove that the discrete Wigner function corresponding to a finite Gaussian is a sum of four products of finite Gaussians. We think that the finite versions of the mathematical formalisms used in quantum mechanics will play an important role, and our aim is to find new useful elements.
|
|
|
|