About this package

This package enables a function giving the matrix elements of the Wigner rotation operator.

Functions

• WignerD[{k_,m_,n_}, {alpha_,beta_,gamma_}]
  
• WignerD[{k_,m_,n_}, beta_]
  
• RotateTensor[a_List, k_Integer, {alpha_, beta_, gamma_}]
  
  
  

Examples

Loading package

<<"(Path to Wigner.m)/Wigner.m"

If you have put "Wigner.m" under directory c:\math\packages, the following command will do.



<<"c:/math/packages/Wigner.m"

Wigner rotation matrix acting on spherical irreducible tensors.

• The (-1,1) element of the rotation matrix for an Euler rotation of the angle (α, β, γ) can be obtained as follows:
  
  

  WignerD[{1,1,-1}, {α,β,γ}]

  
  
  
• If you need the Wigner matrix itself, then type as follows.

  Table[ WignerD[{1, i, j }, {α,β,γ}], {i, -1, 1}, {j, -1, 1}] // TableForm

  
  
  Another example is the Wigner matrix for a 2nd rank spherical tensor.

  Table[ WignerD[{2, i, j }, {α,β,γ}], {i, -2, 2}, {j, -2, 2}] // TableForm

  Extension to the 3rd rank tensor, 4th rank tensor, ... is straightforward.
  
  
• The reduced Wigner rotation matrix for the β rotation alone is obtained with WignerD[{k, m, n}, β] instead of WignerD[{k, m, n}, {α,β,γ}].

Version information

• Version1.1 : October 2005
• Version1.0 : September 1996