Bad Qubits — Learn Quantum by Doing

Multiple choice

Using J = L + S, the spin-orbit operator L.S can be rewritten so that on a coupled state |j, m_j> its expectation value depends only on j, ell, and s. Which identity gives this?

L.S = (1/2)(J^2 - L^2 - S^2)
L.S = L^2 + S^2 - J^2
L.S = J^2 - L^2 - S^2
L.S = (1/2)(J^2 + L^2 + S^2)