An electron is at rest in an oscillating magnetic field along the z-direction with B,=Bo cos(wt) where Bo and w are constants. a. Write the Hamiltonian matrix for this spin system. (5 Pts) b. The electron starts out at t=0 in the spin-up state with respect to the x-axis, that is x(0)-x.) Determine y(1) at any subsequent time. Hint. Solve the time-dependent Schrodinger equation directly. (10 Pts) c. Find the probability of getting -hbar/2 (hbar=h/27) if you measure S, (10 Pts) d. What is the minimum field (Bo) required to force a complete flip in S.. (5 Pts)