# Component

Component[tens,q]

extracts the q‐th component of a spherical tensor tens.

Component[cart,i]

extracts the i‐th component of a Cartesian vector cart.

Component[decomp, k]

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

Component[op,{m_{1},m_{2}}]

extracts the matrix element corresponding to sublevels with angular‐momentum‐projection quantum numbers m_{1} and m_{2} from an operator op.

Component[sys,op,{s_{1},s_{2}}]

extracts the matrix element of operator op corresponding to the states s_{1} and s_{2} of atomic system sys.

Component[sys,mat,{s_{1},s_{2}}]

extracts the tensor decomposition from the tensor‐decomposition matrix mat corresponding to the states s_{1} and s_{2}.

# 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 m
_{i}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 n
_{i}may be given as Component[tens,n_{1},n_{2},…] or Component[sys,tens,n_{1},n_{2},…] to extract a component from a nested tensor structure. The index n_{1}refers to the top-level tensor, the index n_{2}to the second level, and so on. - Component[tens] extracts the single component from a rank‐zero tensor, the single matrix element from a rank-zero operator, or the single tensor decomposition from a tensor‐decomposition matrix for a single angular-momentum state.