3. (15 points) Positronium is a system consisting of an electron and its anti-particle, a positron, bound together into an exotic atom. The effective Hamiltonian for this system in the ground state, 1S, when embedded in a constant magnetic B = (0, 0, B) is H = Eo + DS1 . S2 + 2/BB(S1z - S2z)/h (a) Find the energy eigenvalues and eigenstates of the triplet and singlet states when B = 0. (b) Use first order perturbation theory to find the energy eigenvalues for B * 0