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A python library to compute the Wigner 3j and 6j symbols with very large l values. All the calculation is carried out in C++. Under the hood C++ code made by Joey Dumont (github user valandil).

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Wigner Symbols

A C++ ensemble of functions to compute the Wigner 3j- and 6j- symbols. It implements the algorihtm designed by Schulten and Gordon. It can either compute an array of Wigner 3j or 6j symbols, or a single coefficient. It also computes the Clebsch-Gordan coefficients.

API documentation

We list the user-facing functions that compute the Wigner symbols. The functions are behind the namespace WignerSymbols.

  • std::vector<double> wigner3j(double l2, double l3, double m1, double m2, double m3)
    Computes Wigner 3j symbols with all possible values of l1. Returns an std::vector<double> with the coefficients sorted by increasing values of l1.
  • double wigner3j(double l1, double l2, double l3, double m1, double m2, double m3)
    Computes a specific Wigner 3j symbol.
  • double clebschGordan(double l1, double l2, double l3, double m1, double m2, double m3)
    Computes a specific Clebch-Gordan coeffcient.
  • std::vector<double> wigner6j(double l2, double l3, double l4, double l5, double l6)
    Computes Wigner 6j symbols with all possible values of l1. Returns an std::vector<double> with the coefficients sorted by increasing values of l1.
  • double wigner6j(double l1, double l2, double l3, double l4, double l5, double l6)
    Computes a specific Wigner 6j symbol.

Bibliography

  • K. Schulten and R. G. Gordon, Recursive evaluation of 3j and 6j coefficients, Comput. Phys. Commun. 11, 269–278 (1976).
  • K. Schulten, Exact recursive evaluation of 3j- and 6j-coefficients for quantum-mechanical coupling of angular momenta, J. Math. Phys. 16, 1961 (1975).

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A python library to compute the Wigner 3j and 6j symbols with very large l values. All the calculation is carried out in C++. Under the hood C++ code made by Joey Dumont (github user valandil).

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