Weyl quantization

E117657
mathematical formalism in quantum mechanics phase-space quantization method quantization scheme

Weyl quantization is a mathematical procedure in quantum mechanics that systematically associates classical observables with quantum operators in a symmetric and coordinate-independent way.

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All labels observed (4)

Label Occurrences
Weyl quantization canonical 3
Weyl calculus 1
Weyl transform 1

Statements (47)

Predicate Object
instanceOf mathematical formalism in quantum mechanics ⓘ
phase-space quantization method ⓘ
quantization scheme ⓘ
alternativeTo anti-normal (Berezin–Toeplitz) quantization ⓘ
normal ordering quantization ⓘ
assumes canonical position and momentum variables ⓘ
basedOn classical phase space ⓘ
symplectic structure ⓘ
characterizedBy self-adjoint operators for real classical observables ⓘ
use of mid-point rule in phase space ⓘ
compatibleWith symplectic covariance ⓘ
definedOn cotangent bundle of configuration space ⓘ
ensures symmetric ordering of position and momentum operators ⓘ
field mathematical physics ⓘ
operator theory ⓘ
quantum mechanics ⓘ
symplectic geometry ⓘ
formalismType phase-space operator correspondence ⓘ
generalizes canonical quantization ⓘ
hasProperty coordinate-independent ⓘ
invertible on suitable function spaces ⓘ
linear ⓘ
symmetrically ordered ⓘ
influenced modern deformation quantization theory ⓘ
introducedBy Hermann Weyl ⓘ
introducedIn 1920s ⓘ
maps classical observables to quantum observables ⓘ
mapsFrom functions on phase space ⓘ
mapsTo operators on Hilbert space ⓘ
namedAfter Hermann Weyl ⓘ
relatedTo Moyal product ⓘ
Weyl quantization self-linksurface differs ⓘ
surface form: Weyl calculus

Wigner distribution function ⓘ
surface form: Wigner quasi-probability distribution

Wigner distribution function ⓘ
surface form: Wigner–Weyl transform

deformation quantization ⓘ
pseudodifferential operators ⓘ
satisfies correspondence principle in semiclassical limit ⓘ
usedIn microlocal analysis ⓘ
quantum chaos ⓘ
semiclassical analysis ⓘ
signal processing ⓘ
usesConcept Fourier analysis ⓘ
surface form: Fourier transform

Lie group ⓘ
surface form: Heisenberg group

canonical commutation relations ⓘ
classical observable ⓘ
phase-space function ⓘ
quantum operator ⓘ

Referenced by (6)

Full triples — surface form annotated when it differs from this entity's canonical label.

Hermann Weyl → knownFor → Weyl quantization ⓘ
Wigner distribution function → relatedTo → Weyl quantization ⓘ
this entity surface form: Weyl transform
Wigner distribution function → relatedTo → Weyl quantization ⓘ
this entity surface form: Weyl–Wigner phase-space formulation of quantum mechanics
Weyl → knownFor → Weyl quantization ⓘ
subject surface form: Hermann Weyl
Gruppentheorie und Quantenmechanik → relatedConcept → Weyl quantization ⓘ
Weyl quantization → relatedTo → Weyl quantization self-linksurface differs ⓘ
this entity surface form: Weyl calculus