Quantum Mechanics Problem. Help!! Hey gang, This is a physicsGRE problem ( GR9677 question #77 ) that I have yet to see anyone answer well. Please let me know if I'm not being clear. Here goes: Question: "Two ions, 1 and 2, at fixed separation, with spin angular momentum operators S_1 and S_2, have the interaction Hamiltonian H = -JS_1 (dot) S_2, where J > 0. The values of (S_1)^2 and (S_2)^2 are fixed at S_1(S_1 + 1) and S_2(S_2 + 1), respectively. Which of the following is the energy of the ground state of the system?" Ok, that's the question. The answer is: -(J/2)[( S_1 + S_2)( S_1 + S_2 + 1) - S_1(S_1 + 1) - S_2(S_2 + 1)] How did we get this answer? Can someone fill in the steps?