THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION.

DOCUMENTATION CENTER SEARCH

Mathematica > Mathematics and Algorithms > Mathematical Functions > Special Functions > WignerD >

BUILT-IN MATHEMATICA SYMBOL

WignerD

gives the Wigner D-function

gives the Wigner D-function

gives the Wigner D-function

The Wigner D-function gives the matrix element of a rotation operator parametrized by Euler angles in a -dimensional unitary representation of a rotation group when parameters , , are physical, i.e. all integers or half-integers such that .

Out[1]=

Out[2]=

Evaluate numerically for physical parameters:

Evaluate numerically for unphysical parameters:

Construct a rotation matrix for a spin-1/2 representation:

Check unitarity:

Build a 3D vector from spinors:

Spinor basis translates into coordinate basis:

Coordinate transformation induced by unitary transformation on spinors:

Construct the resulting rotation matrix directly using Euler's angles:

For vanishing parameter

Matrix elements of the Wigner D matrix satisfy certain symmetry relations:

WignerD functions form an orthogonal basis on the

group:

The integral is equal to

The product of two WignerD functions can be expanded in terms of WignerD functions using ClebschGordan coefficients: