GroupTheory`
GroupTheory`

GTAngularMomentumRep

GTAngularMomentumRep[group,j]

gives a (2j+1)-dimensional matrix representation of O(3) using the WignerD-function.

Details and Options

  • With the help of the WignerD-function a matrix representation for any point group can be calculated. The WignerD-function can be calculated using WignerD.
  • The following options can be given:
  • GOFast GOFastValueControls the input validation
    GOHarmonics "Complex"Decides, which kind of spherical harmonics are used
  • See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica, chapter 7.4.

Examples

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Basic Examples  (2)

First, load the package:

A matrix representation corresponding to l=1 is calculated for the point group :

Options  (3)

GOFast  (2)

The evaluation time can be decreased, using GOFastTrue.

If GOFastFalse is used, a check of the input will be performed.

GOHarmonics  (1)

Calculate the transformation matrices of complex spherical harmonics.

Calculate the transformation matrices of real spherical harmonics (tesseral harmonics).