3. Consider an electron in a quantum state that evolves in time according to 12 (t ) ) = - V2 ge - iwot / 2 | Et ) + etiwot / 2 | E- ) , V2 where | E+) and | E-) are energy eigenvectors corresponding to the energy eigenvalues Et = thwo/2. In the z-basis, the Hamiltonian for this system is given by H = " hwo (a) Find (Sz). (Sy), and (S=) for this system. (b) Ehrenfest's Theorem says that the time dependence of an operator, A is It ( 4 ) = - " (14, H] ) + ( 4 ) , where A = . Verify this equation for (Sx), (Sy), (S=) (i.e. evaluate both sides and show they are equal). (Hint: you can find the relationships between spin commutators on pg. 56 in Mcintyre - Eqn. 2.96.) (c) What does this imply about the expectation values of Sx, Sy, and S, in this case