3. A spin-1/2 particle is in a magnetic field B = By3 + By (cos(wt)Z + sin(wt)) . (2) (a) Let . [0(8) = an (e 1/2| 1) + agl)e'=t/?| 1 3) Write the Schroedinger equation for [14(#)), and use this to write the differential equation that the coefficients ay o must satisfy. (Do not solve the Schroedinger equation at this point). (b) From (a), find the wave function in the rotating frame, e.g. find [9(8)) = ()] 1) + az(t)] 4) (4) if the particle starts in the state | |) at time = 0. Hint: One way to do this is to take your differential equation, and write it in the form (art) = 5 (or) where H isa 2 x 2 matrix, which you can think of as the Hamiltonian in the rotating frame. A general form for the eigenvectors of this matrix is given in Eq. 3.57 (see discussion starting at 3.55) in the book. Write your answer in terms of the angle , defined by tan f = w;\"j: () Use your result from (c) to find [()). (d) Compute the probability of finding the system in the state [()) and in the state +) as a function of time, in both (). Which if these answers gives you the actual probability of finding your spin +) if you measure it in the lab