GTProjectionOperator

GTProjectionOperator[group,ireducible representation,m,n,function,arguments]    gives the part of a given function with arguments, which transforms like the m-th row and the n-th column of an irreducible representation.

DetailsDetails

  • The projection operator is given by , where is the dimension of the irreducible representation with matrix elements and is the order of the group. The application of the projection operator to an arbitrary function will result in a function that transforms like the row of the irreducible representation .
  • Typically arguments is a list of Cartesian coordinates:
  • arguments = {x,y,z}
  • The following option can be given:
  • GOFastGOFastValueSkips the input validation
  • See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica, chapter 5.9.

ExamplesExamplesopen allclose all

Basic Examples  (1)Basic Examples  (1)

First, load the package:

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The example is based on the point group . The projection operators concerning to the first row of the irreducible representation are applied to a function. First, the point group and character table are installed and the irreducible representation matrices are calculated.

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The function will be analysed.

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The application of the projection operator, related to the first row and the first column of the irreducible representation can be calculated by:

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The same formalism holds for the second row and the first column:

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