where the prefactor α α determines the strength of the spin-orbit coupling. Now, the new Hamiltonian with this new Δ Δ H SO term does not commute with L and S . It only commutes with L 2 , S 2 , J 2 and J = L + S , which is the total angular momentum operator. In other words, m l , m s are no longer good quantum numbers, but l , s , j , m j are (in addition to the principal quantum number n ).