Particle with spin 1/2 is subject to magnetic field B, which zcomponent Bcosa is time independent, and the field component transverse to z is constant in value but rotates around 2 with frequency 03 (so that the total magnetic field subtends a cone during the period 27t/(0). Assume that at time t=0, transverse component of magnetic field is along x, and the system is in a state with energy uB, which is an eigenstate for magnetic field with components (Bsind, 0, Bcosa). I) Find the time evolution of the state of the system. ll) Assuming that hm is much smaller than 118, find the state at t=ZTE/(0. Separate the obtained phase in two contributions: one that would occur even if the field B were timeindependent and the other, which is related to magnetic field variation. III) For he) arbitrary in value, find the probability for the particle to make a transition to a state with energy -uB at time t