How to calculate the total angular momentum (J) values How can I calculate the values of $J$ (total angular momentum) for a particular term, for instance, ${}^3P$? 
 A: The superscript on the left is always $2S+1$, where $S$ is the total spin. Thus here we have $S = 1$. The letter stands for the orbital angular momentum, with letters $\mathrm{S}$ (not the same $S$ as before!), $\mathrm{P}$, $\mathrm{D}$, ... corresponding to $L = 0$, $L = 1$, $L = 2$, ... Thus we have $L = 1$.
The total angular momentum $J$ is actually not fully determined, in the same sense that knowing the magnitudes of two regular vectors doesn't allow you to know even the magnitude of the sum. $J$ can range from $\lvert L - S \rvert$ to $L + S$, so it can be $0$, $1$, or $2$. One can specify one of these states with a subscript on the right, e.g. ${}^3\mathrm{P}_1$.
A: You can calculate value of J = 2, So it will be 3P2
The spin angular momentum is given by L = |l2-l1|,|l2-l1|+1,.....,l1+l2 = 1,2,3
And hence the values of the total angular momentum S = |s2-s1|,|s2-s1|+1,.....,s1+s2 = 0,1
J = |L-S|,|L-S|+1,.....,L+S = 0,1,2,3,4 
The symbolic way to represent the quantum state with L=1,S=1,J=2, can be represented as 3P2.
