definition 25.52 Wigner function

open in the book · parts/03-classical-mechanics/08-poisson-quantum-bridge.tex:1860 · p. 893

ground object -- no derivation owed

Rests on

depends_on definition 17.29 Fourier transform; the treatise convention ¶
depends_on definition 25.44 Weyl and normal ordering ¶
- depends_on definition 25.42 Ordering rule ¶
  - depends_on corollary 25.41 Quantization is not a functor ¶
    - depends_on theorem 25.38 Groenewold–van Hove ¶
      - depends_on equation 25.31 eq:pq-dirac-rule ¶
      - depends_on theorem 25.34 Stone–von Neumann ¶
      - depends_on theorem 5.160 Schur's second lemma ¶
      - proves proof ch:08-poisson-quantum-bridge@proof-16 ¶
  - depends_on postulate 25.27 Dirac's correspondence rule ¶
    - depends_on equation 22.41 eq:ham-poisson-bracket ¶
    - depends_on theorem 25.3 The bracket is a Lie bracket ¶
      - depends_on equation 22.41 eq:ham-poisson-bracket ¶ ↺
      - depends_on equation 22.56 eq:ham-symplectic-matrix ¶
      - proves proof ch:08-poisson-quantum-bridge@proof-1 ¶

Supports

depends_on definition A.605 The analytic continuation of the overlaps ¶
- depends_on lemma A.606 $F$ is entire, and is the overlap in disguise ¶
  - depends_on lemma A.607 A zero-free entire function is an exponential ¶
    - depends_on proposition A.609 The exponent is a quadratic polynomial ¶
      - depends_on proposition A.611 The constraint on $\Gamma$ ¶

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	Fourier transform; the treatise convention	declared	parts/03-classical-mechanics/08-poisson-quantum-bridge.tex:1876
`depends_on`	→	Weyl and normal ordering	declared	parts/03-classical-mechanics/08-poisson-quantum-bridge.tex:1876
`depends_on`	←	The analytic continuation of the overlaps	declared	appendices/A-long-proofs.tex:28991