I agree that is probably the most straight forward way of going about this, I wanted to try to avoid explicit construction of the Hamiltonian in matrix form though with the hopes of possibly being able to generalize the process. Any hints on the route I was working on the previous post?
Thanks!
I think I partly answered my own question: I guess you can treat (S_1+S_2) + S_3 as an addition of two spin systems? If that is the case then (S_1+S_2)^2|S,m>=h^2(S_1+S_2)(S_1+S_2+1)|S,m>. But then how do we treat S_1 and S_2? And I don't seem to need any C.G. coefficients using this method?
Sorry to revive this thread but I am also trying to work out 3 spin 1/2 particle addition and this comment confused me. How can you find (S_1+S_2)^2 in the |S,m> basis using C.G. coefficients when S represents the total spin S_1+S_2+S_3?