spherical_like_matrix_element
- ryd_numerov.angular.spherical_like_matrix_element(l1, l2, operator, kappa)[source]
Calculate the reduced spherical-like matrix element $(l2||hat{Y}_{k0}||l1)$.
The matrix elements of the spherical operators are given by (see also: Gaunt coefficient)
\[\begin{split}(l2||\hat{Y}_{k0}||l1) = (-1)^l2 \sqrt{(2 * l2 + 1)(2 * l1 + 1)} * \sqrt{\frac{2 * \kappa + 1}{4 \pi}} \begin{pmatrix} l2 & k & l1 \\ 0 & 0 & 0 \end{pmatrix}\end{split}\]If the operator is the electric multipole operator, the prefactor $sqrt{(2 * kappa + 1) / (4 pi)}$ is dropped.
- Parameters:
l1 (
int) – The orbital momentum quantum number of the initial state.l2 (
int) – The orbital momentum quantum number of the final state.operator (
Literal['MAGNETIC','ELECTRIC','SPHERICAL','MAGNETIC_S','MAGNETIC_L']) – The multipole operator, either “SPHERICAL” or “ELECTRIC”.kappa (
int) – The quantum number $kappa$ of the angular momentum operator.
- Return type:
float- Returns:
The reduced matrix element $(l2||hat{Y}_{k0}||l1)$.