GroupTheory`
GroupTheory`

GTBSTOperator

GTBSTOperator[l,m,J]

calculates matrix elements , where is the Buckmaster-Smith-Thornley operator equivalent.

Details and Options

  • The matrix elements are calculated according to Smith and Thornley
  • denotes the reduced matrix element.
  • To calculate a single matrix element refer to GTBSTOperatorElement.
  • See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica, chapter 7.4
  • D. Smith and J. H. M. Thornley, The use of 'operator equivalents', Proceedings of the Physical Society, 1966, 89, 779-781

Examples

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Basic Examples  (1)

First, load the package:

Calculate the matrix ,

Neat Examples  (1)

First, load the package:

As an example, we calculate the crystal field Hamiltonian for the point group .

The crystal field operators can be replaced by the BST operators as follows. We choose l=2 for the example.

Calculating the eigenvalues shows the splitting of the d-states (l=2) into and levels.