Problem # 4: Coupling of Spin-Orbital Angular Momentum (10 points) A particle with spin S = 1 is in a state with an angular momentum of L = 2. The spin-orbit coupling Hamiltonian can be expressed as H = AL . S a) What are the possible energies for this system? (8 points) b) What are the degeneracies for each energy? (2 points) Hint: You need to consider the total angular momentum (] = L + S) since the Hamiltonian involves spin-orbit coupling