GROUP THEORY SYMBOL

GTSymmetryBasisFunctions

GTSymmetryBasisFunctions[character table,wave functions]
calculates to which irreducible representations the wave functions are basis functions.

DetailsDetails

  • In tight-binding theory atomic-like functions are used to build the Hamiltonian. The symmetry of those functions is represented by real linear combinations of spherical harmonics in cartesian coordinates:
  • s1
    p,,
    d,,,,
  • The point group of the crystal is . The character table to is calculated by GTCharacterTable. GTSymmetryBasisFunctions analyzes to which irreducible representations of the functions belong.
  • The following options can be given:
  • GONames{}Controls the names of irreducible representations
    GOVerboseFalseControls the output of additional information
  • See: R.F. Egorv, B.I. Reser, V.P. Shirkovskii,Consistent Treatment of Symmetry in the Tight Binding Approximation, phys. stat. sol. 26, 391 (1968)
  • W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica

ExamplesExamplesopen allclose all

Basic Examples  (1)Basic Examples  (1)

First load the package.

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The point group is considered.

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The character table of the group is calculated. The notation of Mulliken is used.

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The angular parts (spherical harmonics) of the wave functions can be expressed in cartesian coordinates. All functions up to are considered.

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Find out to which irreducible representations the functions belong. (Long output please scroll right.)

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Options  (1)Options  (1)

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