GroupTheory`
GroupTheory`

GTStevensOperator

GTStevensOperator[l,m,J]

calculates the matrix elements , where is the Stevens operator equivalent.

Details and Options

  • The matrix elements are calculated using the method of Ryabov.
  • To calculate only a single matrix element refer to GTStevensOperatorElement.
  • See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica, Chapter 7.4
  • I. Ryabov, On the generation of operator equivalents and the calculation of their matrix elements, Journal of Magnetic Resonance, Elsevier, 1999, 140, 141-145
  • K. W. H. Stevens, Matrix Elements and Operator Equivalents Connected with the Magnetic Properties of Rare Earth Ions, Proceedings of the Physical Society. Section A, 1952, 65, 209

Examples

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Basic Examples  (1)

First, load the package:

Calculate the matrix elements of ,

Applications  (1)

The Stevens operator can be used to calculate the influence of a crystal field in the framework of linear perturbation theory.

Calculate the crystal field Hamiltonian for the point group

Replace the S[l,m] by Stevens operator equivalents, e.g. for d-electrons (l=2).

Now, it is possible to calculate the eigenvalues of the crystal field Hamiltonian directly.