GroupTheory`
GroupTheory`

GTSymmetryBasisFunctions

GTSymmetryBasisFunctions[character table,wave functions]

calculates to which irreducible representations the wave functions are basis functions.

Details and Options

  • 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

Examples

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Basic Examples  (1)

First load the package.

The point group is considered.

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

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

Find out to which irreducible representations the functions belong.

Options  (1)

GONames  (1)

If there is a reason to use other names for the irreducible representations, GONames helps.