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Compared to a short-time Fourier transform, such as the Gabor transform, the Wigner distribution function provides the highest possible temporal vs frequency resolution which is mathematically possible within the limitations of the uncertainty principle.
The Wigner quasiprobability distribution (also called the Wigner function or the Wigner–Ville distribution, after Eugene Wigner and Jean-André Ville) is a quasiprobability distribution. It was introduced by Eugene Wigner in 1932 to study quantum corrections to classical statistical mechanics.
13 de ene. de 2017 · Here we discuss the fundamental properties of the Wigner distribution function. 1. Definition of Wigner function. The Wigner distribution function is a quasi-probability distribution function in phase space. ( x , p ) and is defined by. ( x , p ) dy . ( x y ) e.
Describe the main properties of the Wigner function. Describe the relation between the Wigner function and the probability distribution of a quantum state.
The Wigner distribution and the a ociated Cohen class of generalized Wigner distributions offer a possible way to conduct such analysis. In this article I review some of the basic features of the Wigner distribution and emphasize its relationship to the two-dimensional ambiguity function. I discuss the interference terms that
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As a result, the Wigner function is a mathematical construct intended to characterize the system’s probability distribution simultaneously in the coordinate and the momentum space - for 1D systems, on the phase plane \([X, P]\), which we had discussed earlier - see Fig. 5.8.
The Wigner Distribution. R. F. O’Connell. Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803-4001. In contrast to classical physics, the language of quantum mechanics involves operators and wave functions (or, more generally, density operators).
