wigner_coupling

Wigner 3j coupling functions.

wigner_3j_coupling(wigner_3j_coefficients, ldict, L_R=0)[source]

Compute generalized Wigner symbols for a given L_R. These, like the generalized Clebsch-Gordan coefficients, may be used to reduce products of arbitrary numbers of spherical harmonics.

The approach to construct generalized Wigner symbols is manually defined for each rank for pedagogical and clarity purposes.

TODO: Change name to generalized_wigner_coupling.

Parameters:

  • wigner_3j_coefficients (dict) – Precomputed Wigner 3j coefficients.

  • ldict (dict) – Dictionary of ranks and their corresponding L values.

  • L_R (int) – Resultant angular momentum quantum number. This determines the equivariant character of the rank N descriptor after reduction. L_R=0 corresponds to a rotationally invariant feature, L_R=1 corresponds to a feature that transforms like a vector, L_R=2 a tensor, etc.

Returns:

coupling – Generalized Wigner symbols, {M_R:{rank:{l:{m:coupling_coefficient}}}

Return type:

dict