Wigner distribution function
E98266
mathematical concept
phase-space distribution
quasi-probability distribution
tool in quantum mechanics
tool in signal processing
The Wigner distribution function is a quasi-probability distribution used in quantum mechanics and signal processing to represent quantum states in phase space, often exhibiting non-classical features such as negative values.
All labels observed (4)
| Label | Occurrences |
|---|---|
| Wigner distribution function canonical | 1 |
| Wigner quasi-probability distribution | 1 |
| Wigner–Ville distribution | 1 |
| Wigner–Weyl transform | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T818208 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Wigner distribution function Context triple: [Eugene Wigner, knownFor, Wigner distribution function]
-
A.
Fokker–Planck equation
The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.
-
B.
Wick’s theorem
Wick’s theorem is a fundamental result in quantum field theory that expresses time-ordered products of field operators as sums of normal-ordered products with all possible contractions, forming the basis for deriving Feynman rules and diagrammatic expansions.
-
C.
Fourier analysis
Fourier analysis is a mathematical method for decomposing functions or signals into sums of sinusoidal components, widely used in fields such as signal processing, physics, and engineering.
-
D.
Fourier
Fourier is a French surname most famously associated with Jean-Baptiste Joseph Fourier, the mathematician and physicist known for developing Fourier analysis and Fourier series.
-
E.
Fresnel diffraction theory
Fresnel diffraction theory is a wave-optics framework that describes how light diffracts when source or observation distances are finite, using near-field approximations derived from the Huygens–Fresnel principle.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Wigner distribution function Target entity description: The Wigner distribution function is a quasi-probability distribution used in quantum mechanics and signal processing to represent quantum states in phase space, often exhibiting non-classical features such as negative values.
-
A.
Fokker–Planck equation
The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.
-
B.
Wick’s theorem
Wick’s theorem is a fundamental result in quantum field theory that expresses time-ordered products of field operators as sums of normal-ordered products with all possible contractions, forming the basis for deriving Feynman rules and diagrammatic expansions.
-
C.
Fourier analysis
Fourier analysis is a mathematical method for decomposing functions or signals into sums of sinusoidal components, widely used in fields such as signal processing, physics, and engineering.
-
D.
Fourier
Fourier is a French surname most famously associated with Jean-Baptiste Joseph Fourier, the mathematician and physicist known for developing Fourier analysis and Fourier series.
-
E.
Fresnel diffraction theory
Fresnel diffraction theory is a wave-optics framework that describes how light diffracts when source or observation distances are finite, using near-field approximations derived from the Huygens–Fresnel principle.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical concept
ⓘ
phase-space distribution ⓘ quasi-probability distribution ⓘ tool in quantum mechanics ⓘ tool in signal processing ⓘ |
| definedOn | phase space ⓘ |
| domain | position and momentum variables ⓘ |
| field |
quantum mechanics
ⓘ
signal processing ⓘ time–frequency analysis ⓘ |
| generalizationOf | classical phase-space distribution ⓘ |
| hasApplication |
quantum information processing
ⓘ
quantum state reconstruction ⓘ radar signal processing ⓘ speech analysis ⓘ time–frequency filtering ⓘ |
| hasProperty |
bilinear in the wavefunction
ⓘ
can exhibit interference fringes ⓘ can take negative values ⓘ covariant under phase-space translations ⓘ marginals reproduce position and momentum distributions ⓘ non-classical features ⓘ normalized to one for pure states ⓘ not a true probability distribution ⓘ real-valued function ⓘ satisfies quantum Liouville equation ⓘ |
| introducedBy | Eugene Wigner ⓘ |
| introducedIn | 1932 ⓘ |
| namedAfter | Eugene Wigner ⓘ |
| relatedTo |
Glauber–Sudarshan P function
ⓘ
Husimi Q function ⓘ Moyal bracket ⓘ Weyl quantization ⓘ
surface form:
Weyl transform
Weyl quantization ⓘ
surface form:
Weyl–Wigner phase-space formulation of quantum mechanics
Wigner distribution function self-linksurface differs ⓘ
surface form:
Wigner–Ville distribution
|
| represents |
quantum states in phase space
ⓘ
time–frequency content of signals ⓘ |
| satisfies | correct classical limit for large quantum numbers ⓘ |
| usedFor |
analyzing non-classical states of light
ⓘ
quantum chaos studies ⓘ quantum optics ⓘ quantum tomography ⓘ semiclassical approximations ⓘ signal analysis with high time–frequency resolution ⓘ studying quantum coherence ⓘ time–frequency representation of signals ⓘ visualizing quantum states ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Wigner distribution function Description of subject: The Wigner distribution function is a quasi-probability distribution used in quantum mechanics and signal processing to represent quantum states in phase space, often exhibiting non-classical features such as negative values.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Wigner–Ville distribution
this entity surface form:
Wigner–Weyl transform
this entity surface form:
Wigner quasi-probability distribution