Forest AngMomRecoupling

The recoupling of two subsystems $\psi$ with angular momenta $j_1$ and $j_2$ to a new system$\Psi$ with total angular momentum $J$ is written as

$\Psi^{J}_{M} = \sum_{m_1,m_2} C^{j_1,j_2,J}_{m_1,m_2,M} \psi^{j_1}_{m_1} \psi^{j_2}_{m_2}$

$C^{j_1,j_2,J}_{m_1,m_2,M}$ : Clebsch-Gordon Coefficient

$C^{1,1/2,3/2}_{1,1/2,3/2}=1$

$C^{1,1/2,3/2}_{1,-1/2,1/2}= \frac{1}{\sqrt{3}}$