triqs.operators.util.U_matrix.angular_matrix_element

triqs.operators.util.U_matrix.angular_matrix_element(l, k, m1, m2, m3, m4)

Calculate the angular matrix element

\[\begin{split}(2l+1)^2 \begin{pmatrix} l & k & l \\ 0 & 0 & 0 \end{pmatrix}^2 \sum_{q=-k}^k (-1)^{m_1+m_2+q} \begin{pmatrix} l & k & l \\ -m_1 & q & m_3 \end{pmatrix} \begin{pmatrix} l & k & l \\ -m_2 & -q & m_4 \end{pmatrix}.\end{split}\]

Parameters:

• l (integer)

• k (integer)

• m1 (integer)

• m2 (integer)

• m3 (integer)

• m4 (integer)

Returns:

ang_mat_ele – Angular matrix element.

Return type:

scalar