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WignerEckart[sys, {op, k}] returns the covariant tensor representing the rank-k operator op with respect to the basis states of the atomic system sys. |

WignerEckart[sys, {op, k, q}] returns the q-th component of the tensor operator. |

WignerEckart[state_{1}, {op, k, q}, state_{2}]returns the matrix element of the operator between the atomic states state _{1} and state_{2}. |

WignerEckart[j, {op, k}] returns the operator for a Zeeman system with angular momentum equal to integer or half-integer j. |

- WignerEckart finds the matrix elements of an operator in terms of the reduced matrix element of using the Wigner—Eckart theorem:

- Reduced matrix elements for some operators are defined in the ADM package. If an unknown operator is supplied, the matrix elements will be written in terms of placeholder values for the reduced matrix elements.

- Operators with defined reduced matrix elements include Energy, Polarization, J, L, S, Dipole, MagneticMoment, Polarizability, GroundState and ExcitedState.

- WignerEckart takes the following options:

Representation | Automatic | the basis to represent the tensor operator | |

AllowedCouplings | All | matrix elements that are allowed to be nonzero |

- Representation takes the values "Zeeman", "PolarizationMoments", or Automatic, where Automatic means that the default option value set for DensityMatrix is used.