[NOTES/QM-17009] Addition of Angular Momenta Using Tables

Using tables of Clebsch Gordon Coefficients

We shall now take up an example of constructing the states $\ket{JM}$ using the tables of Clebsch Gordon coefficients. There are two tables of Clebsch Gordon coefficients given at the end. Note that the first table is for $j_2=\frac{1}{2}$ and the second one for $j_2=1$. For $j_2=\frac{1}{2}$, the two columns correspond to the two values, $\frac{1}{2}$ and $-\frac{1}{2}$, of $m_2$. The two rows correspond to the two possible values of total angular momentum $J=j_1+ \frac{1}{2}$ and $J=j_1-\frac{1}{2}$. Similarly, the second table, corresponding to $j_2=1$, has three columns for the three values $m_2=1,0,-1$ and the three rows correspond to three allowed values $J=j_1+1,j_1,j_1-1$ of total angular momentum.

\input{qm-ymp-17001}

\subsection{Tables of Clebsch Gordon Coefficients}
\input{cg.tex}