The Wigner D-matrix is a unitary matrix in an irreducible representation of the groups SU(2) and SO(3). It was introduced in 1927 by Eugene Wigner, and...

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The expression (1) allows the expression of the Wigner d-matrix d m ′ , m j ( ϕ ) {\displaystyle d_{m',m}^{j}(\phi )} (for 0 ≤ ϕ ≤ 4 π {\displaystyle...

The Wigner quasiprobability distribution (also called the Wigner function or the Wigner–Ville distribution, after Eugene Wigner and Jean-André Ville)...

In relativistic quantum mechanics and quantum field theory, the Bargmann–Wigner equations describe free particles with non-zero mass and arbitrary spin...

number Azimuthal quantum number Table of Clebsch–Gordan coefficients Wigner D-matrix Wigner–Eckart theorem Angular momentum diagrams (quantum mechanics) Clebsch–Gordan...

Wigner D-matrix, an irreducible representation of the rotation group SO(3) This disambiguation page lists articles associated with the title Wigner distribution...

and physics: Wigner D-matrix, represent spins and rotations of quantum states and tensor operators. Higher spin alternating sign matrix Spin group Spin...

scientists Wigner, Eisenbud, Breit, Blatt, Weisskopf, and others. Related theories are U-matrix, S-matrix, by M-matrix, or T-matrix. The term R-matrix is used...

his free central limit theorem had appeared before in Wigner's semi-circle law in the random matrix context. In the field of computational neuroscience...

where D m m ′ ( ℓ ) ( R ) ∗ {\displaystyle D_{mm'}^{(\ell )}({\mathcal {R}})^{*}} is the complex conjugate of an element of the Wigner D-matrix. In particular...

The Wigner–Eckart theorem is a theorem of representation theory and quantum mechanics. It states that matrix elements of spherical tensor operators in...

} is Wigner's small d-matrix. Note that for γ = 2π and α = β = 0; i.e., a full rotation about the z axis, the Wigner D-matrix elements become D m ′ m...

In quantum mechanics, the Wigner–Weyl transform or Weyl–Wigner transform (after Hermann Weyl and Eugene Wigner) is the invertible mapping between functions...

follows, when the states transform under the unitary Wigner D-matrix D ( R ) {\displaystyle {\mathcal {D}}(R)} , where R is a (3×3 rotation) group element...

the random matrix approach infinity. The distribution of the spacing or gaps between eigenvalues is addressed by the similarly named Wigner surmise. Because...

degenerate energy for K=0. Here DJMK is an element of the Wigner D-matrix. The first-order perturbation matrix on basis of the unperturbed rigid rotor function...

density matrix operator may also be realized in phase space. Under the Wigner map, the density matrix transforms into the equivalent Wigner function...

{\hat {\mathcal {P}}}_{i}} on the Wigner D-matrix is simple. In particular P 2 D m ′ m j ( α , β , γ ) ∗ = ℏ 2 j ( j + 1 ) D m ′ m j ( α , β , γ ) ∗ with P...

Wigner's friend is a thought experiment in theoretical quantum physics, first published by the Hungarian-American physicist Eugene Wigner in 1961, and...

analysis techniques and their applications" (CRC Press, 2023). "Wigner-Specific Research". Wigner Initiative. Retrieved 27 January 2025. "Neural Dynamics of...

characteristic values of a symmetric matrix with random coefficients. — Eugene Wigner, Results and theory of resonance absorption Wigner semicircle distribution Mehta...

m\rangle } Introducing the Wigner D matrix elements: D ( R ) m ′ m ( j ) = ⟨ j , m ′ | U ( R ) | j , m ⟩ {\displaystyle {D(R)}_{m'm}^{(j)}=\langle j,m'|U(R)|j...

a Lie group List of Lie group topics Symmetry in quantum mechanics Wigner D-matrix Hall 2015 Corollary 3.51 Hall 2015 Theorem 4.28 Hall 2015 Section 10...

quasi-probability distribution Wigner's friend Wigner's theorem Wigner crystal Wigner D-matrix Wigner effect Wigner energy Wigner lattice Wigner poisoning, Xe-135...

Liouville flow. This formula results from applying the Wigner transformation to the density matrix version of the quantum Liouville equation, the von Neumann...

Thomas–Wigner rotation or Wigner rotation. If a sequence of non-collinear boosts returns an object to its initial velocity, then the sequence of Wigner rotations...

information for ρ 0 {\displaystyle \rho _{0}} . Density matrix π {\displaystyle \pi } can be, for example, I d e n t i t y / dim ⁡ H {\displaystyle {\rm {Identity}}/\dim...

three years later Fierz and Pauli rederived the same equation. The Bargmann–Wigner equations were found in 1948 using Lorentz group theory, applicable for...

procedure, any direct product representation is easily reduced. Wigner D-matrix Tensor operator Wigner–Eckart theorem Representation theory Racah W-coefficient...