Wigner distribution
Encyclopedia
The Wigner distribution is either of two things:
- Wigner semicircle distribution - A probability function used in mathematics (Eugene Wigner)
- Wigner quasi-probability distributionWigner quasi-probability distributionThe Wigner quasi-probability distribution is a quasi-probability distribution. It was introduced by Eugene Wigner in 1932 to study quantum corrections to classical statistical mechanics...
- A distribution in phase spacePhase spaceIn mathematics and physics, a phase space, introduced by Willard Gibbs in 1901, is a space in which all possible states of a system are represented, with each possible state of the system corresponding to one unique point in the phase space...
encoding, in a convenient representation, properties of quantum-mechanical wave-functions. Strictly speaking, it is the Wigner map of the density matrixDensity matrixIn quantum mechanics, a density matrix is a self-adjoint positive-semidefinite matrix of trace one, that describes the statistical state of a quantum system...
in the Weyl correspondenceWeyl quantizationIn mathematics and physics, in the area of quantum mechanics, Weyl quantization is a method for systematically associating a "quantum mechanical" Hermitian operator with a "classical" kernel function in phase space invertibly...
. In signal analysis, it is known as the Wigner-Ville distribution. It is useful in quantum statistical mechanics, quantum chemistry, optics, quantum computing etc. (Eugene Wigner, Hermann WeylHermann WeylHermann Klaus Hugo Weyl was a German mathematician and theoretical physicist. Although much of his working life was spent in Zürich, Switzerland and then Princeton, he is associated with the University of Göttingen tradition of mathematics, represented by David Hilbert and Hermann Minkowski.His...
, J. Ville) - See also Breit–Wigner distribution