extracts the qth component of a spherical tensor tens.


extracts the ith component of a Cartesian vector cart.

Component[decomp, k]

extracts the spherical tensor of rank k from a tensor decomposition decomp.


extracts the matrix element corresponding to sublevels with angularmomentumprojection quantum numbers m1 and m2 from an operator op.


extracts the matrix element of operator op corresponding to the states s1 and s2 of atomic system sys.


extracts the tensor decomposition from the tensordecomposition matrix mat corresponding to the states s1 and s2.

Details and Options

  • The component index q must be a integer or half-integer from the range , where is the rank of the spherical tensor.
  • The quantum numbers mi be a integers or half-integers from the range , where is the rank of the operator.
  • The Cartesian component index i must be a positive integer.
  • Additional indices or states ni may be given as Component[tens,n1,n2,] or Component[sys,tens,n1,n2,] to extract a component from a nested tensor structure. The index n1 refers to the top-level tensor, the index n2 to the second level, and so on.
  • Component[tens] extracts the single component from a rankzero tensor, the single matrix element from a rank-zero operator, or the single tensor decomposition from a tensordecomposition matrix for a single angular-momentum state.


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Basic Examples  (1)

The component of a Cartesian vector:

The component of a contravariant spherical tensor:

The component of a covariant tensor operator:

The matrix element of an operator on a angular-momentum space:

The rank tensor from a contravariant spherical-tensor decomposition:

Scope (1)

The component of a Cartesian vector operator:

The matrix element of an operator:

The tensor decomposition of a tensor decomposition matrix:

The component of the rank spherical tensor of the tensor decomposition: