Griffiths Introduction to Elementary Particles · Problem 4.9
Bound States — David J. Griffiths
Physics — QFT · adding-angular-momenta
Problem
When you're adding angular momenta, using equation (4.12), it is useful to check your results by counting the number of states before and after the addition. For instance, in Example 4.1 we had two quarks to begin with, each could have ms=+21 or ms=−21, so there were four possibilities in all. After adding the spins, we had one combination with spin 1 (hence ms=1,0, or −1) and one with spin 0 (ms=0)—again, four states in all.
(a) Apply this check to Example 4.2.
(b) Add angular momenta 2, 1, and 21: list the possible values of the total angular momentum, and check your answer by counting states.