a) Write the Dirac equation in Hamiltonian form by isolating the time-derivative of the spinor on the left-hand side of the equation. The Hamiltonian H will be the operator on the right-hand side of the equation. What is H?
b) Find the commutator of H with the orbital angular momentum operator L.
c) Find the commutator of H with the spin angular momentum operator S.
d) Find the commutator of H with the total angular momentum operator J = L + S.
e) Show that all spinors are eigenstates of SS = S^2. Since S^2 = hss + 1, what is the value of s for a Dirac spinor?