Decomposition

Decomposition[op]
returns the expansion coefficients of the decomposition of a rank-J operator op (e.g., the density matrix) as a sum of polarization moments.
Decomposition[sys, op]
returns a matrix of expansion coefficients for the decomposition of an operator on an atomic system sys.
  • Decomposition returns either a single tensor decomposition object or a matrix of such objects, each consisting of a list of (contravariant) spherical tensors of increasing rank.
  • The decomposition of a rank-J operator [i.e., a (2 J+1)⨯(2 J+1) matrix] is a list of 2 J+1 spherical tensors of rank zero through 2 J.
  • TensorForm can be used to display a tensor decomposition as a list of row or column vectors.
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The tensor decomposition of a J=1 operator:
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Display the decomposition as a list of column vectors using TensorForm:
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Check that it has the form of a contravariant tensor decomposition:
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An atomic system consisting of a J=1 state and a J=0 state:
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Find the matrix of tensor decompositions for the density matrices of the two states and the coherences between the states:
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Check that it has the form of a matrix of tensor decompositions:
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