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.
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
NERFINISHED
→
|
| introducedIn |
1932
→
|
| namedAfter |
Eugene Wigner
NERFINISHED
→
|
| relatedTo |
Glauber–Sudarshan P function
NERFINISHED
→
Husimi Q function → Moyal bracket NERFINISHED → Weyl transform NERFINISHED → Weyl–Wigner phase-space formulation of quantum mechanics NERFINISHED → Wigner–Ville distribution NERFINISHED → |
| 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 → |
Referenced by (1)
| Subject (surface form when different) | Predicate |
|---|---|
|
Eugene Wigner
→
|
knownFor |