WignerEckart

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[state1, {op, k, q}, state2]
returns the matrix element of the operator between the atomic states state1 and state2.
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 A in terms of the reduced matrix element of A using the Wigner—Eckart theorem:
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  • 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.
  • WignerEckart takes the following options:
RepresentationAutomaticthe basis to represent the tensor operator
AllowedCouplingsAllmatrix elements that are allowed to be nonzero
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Define a J=1J=0 system:
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Matrix elements of the Energy operator for the system:
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The three covariant components of the J operator in the spherical basis:
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If an unknown operator is supplied, the result is in terms of the symbolic reduced matrix elements:
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A single matrix element:
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The J operator for a generic Zeeman system with :
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