GroupTheory`
GroupTheory`

GTClebschGordanSum

GTClebschGordanSum[rep1,rep2]

gives the direct sum of two representations rep1 and rep2.

Details and Options

  • Considering two arbitrary matrix representations and of the same group. The Clebsch-Gordan sum gives a matrix representation of the form .
  • Alternatively, the symbol can be used instead of the command GTClebschGordanSum.
  • The following option can be given:
  • GOFast GOFastValueSkips the input validation
  • See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica, chapter 5.2.

Examples

open allclose all

Basic Examples  (1)

First, load the package:

During the example we calculate the Clebsch-Gordan sum of the representation given by rotation matrices and of the angular momentum representation with l=1 for the point group .

Options  (3)

GOFast  (3)

First, load the package:

Then run the examples:

The evaluation time can be decreased, using GOFastTrue.

If GOFastFalse is used, it will be checked if the input is a group.

If GOFastFalse is used, it will be checked if the group order of the irreducible representations is equal to each other.