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The Wigner semicircle distribution, named after the physicist Eugene Wigner, is the probability distribution on [− R, R] whose probability density function f is a scaled semicircle (i.e., a semi-ellipse) centered at (0, 0): for − R ≤ x ≤ R, and f (x) = 0 if |x| > R. The parameter R is commonly referred to as the "radius" parameter of ...
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. The goal was to link the wavefunction that ...
The Wigner distribution function is not a linear transform. A cross term ("time beats") occurs when there is more than one component in the input signal, analogous in time to frequency beats. [1] In the ancestral physics Wigner quasi-probability distribution, this term has important and useful physics consequences, required for faithful ...
The relativistic Breit–Wigner distribution (after the 1936 nuclear resonance formula [ 1 ] of Gregory Breit and Eugene Wigner) is a continuous probability distribution with the following probability density function, [ 2 ] where k is a constant of proportionality, equal to. with. (This equation is written using natural units, ħ = c = 1.)
Since the Wigner representation is the most common, this article will usually stick to it, unless otherwise specified. The phase-space distribution possesses properties akin to the probability density in a 2n-dimensional phase space. For example, it is real-valued, unlike the generally complex-valued wave function. We can understand the ...
Modified Wigner distribution function. A Modified Wigner distribution function is a variation of the Wigner distribution function (WD) with reduced or removed cross-terms. The Wigner distribution (WD) was first proposed for corrections to classical statistical mechanics in 1932 by Eugene Wigner. The Wigner distribution function, or Wigner ...
Wigner distribution or Wigner function may refer to: Wigner quasiprobability distribution (what is most commonly intended by term "Wigner function"): a quasiprobability distribution used in quantum physics, also known at the Wigner-Ville distribution. Wigner distribution function, used in signal processing, which is the time-frequency variant ...
The kernel of the Wigner distribution function (WDF) is one. However, no particular significance should be attached to that, since it is possible to write the general form so that the kernel of any distribution is one, in which case the kernel of the Wigner distribution function (WDF) would be something else. Characteristic function formulation