Mat2sphten.m

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Converts a 3x3 interaction matrix into the irreducible spherical tensor notation: one rank 0 component, three rank 1 components and five rank 2 components to the total of nine independent components.

The components are listed in the following order:

rank 0: (0,0)
rank 1: (1,1) (1,0) (1,-1)
rank 2: (2,2) (2,1) (2,0) (2,-1) (2,-2)

and are returned as coefficients in front of the corresponding irreducible spherical tenror operators. Syntax:

                   [rank0,rank1,rank2]=mat2sphten(M)

Outputs:

  rank0      - a single number giving the coefficient of T(0,0) in
               the spherical tensor expansion.
  rank1      - a row vector with three numbers giving the coeffici-
               ents of T(1,1), T(1,0) and T(1,-1) in the spherical
               tensor expansion.
  rank2      - a row vector with five numbers giving the coeffici-
               ents of T(2,2), T(2,1), T(2,0), T(2,-1) and T(2,-2)
               in the spherical tensor expansion.

See Table 1 in http://dx.doi.org/10.1016/0022-2364(77)90011-7 (note that minus signs are absorbed into the coefficients in Spinach).