Please help with the following QM question regarding the Larmor precession.

Suppose that a spin1/2 particle is in the magnetic eld B = B0)\": and subject to the Hamiltonian H = 7B ' S, with S the particle's spin vector. (a) What are the possible energies that could be observed in this system? (b) Work in the normal basis where |1/2, 1/2) = (10)T and |1/2, 71/2) = (0 1)T. Compute the eigenstates of the Hamiltonian, letting the eigenstate X be the eigenstate with the lowest energy and X+ be the one with the highest. (0) Suppose that at t = 0 we prepare an electron in the state W03 2 0)) = (10)T (i.e., spinup in the Zdirection). At time t > 0 what is the probability to measure the particle to be spin down