AtomicDensityMatrix`
AtomicDensityMatrix`

Recomposition

Recomposition[decomp]

returns the reducible operator corresponding to tensor decomposition decomp represented on a space with smallest angular momentum sufficient to support all moments.

Recomposition[j,decomp]

returns the reducible operator on a space with angular momentum j corresponding to tensor decomposition decomp.

Recomposition[sys,mat]

returns the operator for atomic system sys corresponding to the matrix of tensor decompositions mat.

Recomposition[j,tens]

returns the operator that has the spherical tensor tens as the only nonzero component of its tensor decomposition.

Details and Options

  • A tensor decomposition is a list of spherical tensors of increasing rank.

Examples

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Basic Examples  (2)

A tensor decomposition:

Construct the reducible operator in a J=1/2 representation:

An operator on a space that contains only the kappa=2, q=0 polarization moment in its decomposition:

Scope  (1)

Properties & Relations  (3)

Recomposition undoes Decomposition:

Decomposition undoes Recomposition:

The Recomposition of the Hermitian conjugate is the Hermitian conjugate of the Recomposition:

Possible Issues  (1)

If J is specified, it must be at least twice the highest-rank polarization moment to be recomposed: