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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 [1] to study quantum corrections to classical statistical mechanics.
13 de ene. de 2017 · 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. ipy / ( x . ) . ( x , p ) dq . ( p q ) e. 2 ixq / ( p q ) . It is a generating function for all spatial autocorrelation function of a given quantum mechanica;
The Wigner distribution function (WDF) is a quadratic time-frequency distribution (Wigner, 1932; Hlawatsch & Boudreaux-Bartels, 1992; Classen & Mecklenbrauker, 1980). It is defined as (31) W f ( t , ω ) = 1 / 2 π · ∫ − ∞ ∞ f ( t + τ / 2 ) · f ∗ ( t − τ / 2 ) · e − j ω τ · d τ = 1 / 2 π · ∫ − ∞ ∞ F ( ω + η ...
Learning goals. After this lecture you will be able to: Describe the main properties of the Wigner function. Describe the relation between the Wigner function and the probability distribution of a quantum state.
For this two-dimensional scalar eld, the Wigner distribu-tion is a four-dimensional function that describes the eld's positional information along two of the axes and its fre-quency information along the other two. Let us assume we have narrowband polychromatic light.
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.
