# How to calculate Clebsch-Gordon coefficients

by Avijeet
Tags: clebschgordon, coefficients
CG coeffs are the scalar products of the description between the uncoupled and coupled representations for two angular momentum vectors j1 and j2. In usual notation, $<j_1m_1j_2m_2|j_1j_2JM>$, the uncoupled representation is on the left, where the z-projections of the two angular momenta are considered separately. The coupled representation is on the right, where the two angular momenta are first added together to give total angular momentum (J), and it's projection on the z-axis (M). Remember there are multiple ways that two angular momenta can be added ... that is the reason we need the CG coefficients in the first place.