please answer this question as soon as you can

Question 3 (7 points) Suppose a spin 1/2 system is initialized to an eigenstate of 339. In\") : lr+> : 1mm+>+ 27>)- a) At time 1' : 0 we apply a. magnetic eld along the direction such that the Hamiltonian is now H : wogz. Determine the time evolution of the system '60)) (4 points). 1)) Find the probability of measuring; the system in |z+> as a function of time (3 points)