treams.special.wignersmalld

treams.special.wignersmalld(l, m, k, theta) = <ufunc 'wignersmalld'>

Wigner-d matrix element

Wigner-(small)-d symbol \(d^l_{mk}(\theta)\) calculated via forward or backward recursion for integer arguments. The decision is based on the number of recursive function calls necessary. The function return values are cached during recursion.

Note

Mathematica and Dachsela use a different sign convention, which means taking the negative angle.

Parameters:

• l (integer) – Degree \(l \geq 0\)

• m (integer) – Order \(|m| \leq l\)

• k (integer) – Order \(|k| \leq l\)

• theta (float or complex)

Returns:

float or complex

References

• Wikipedia: Wigner D-matrix

• H. Dachsela, J. Chem. Phys. 142, 144115 (2006)