1. Consider a spin 1/2 particle of magnetic moment M = yS. The spin state space is spanned by the basis of the + and -> vectors, eigenvectors of S. with eigenvalues + h/2 and -h/2. At time t = 0, the state of the system is : | 4(1 = 0) > = | +> a. If the observable S is measured at time t = 0, what results can be found, and with what probabilities? b. Instead of performing the preceding measurement, we let the system evolve under the influence of a magnetic field parallel to Oy, of modulus Bo. Calculate, in the {| + >, | > } basis, the state of the system at time t. c. At this time t, we measure the observables S, S, S. What values can we find, and with what probabilities? What relation must exist between Bo and for the result of one of the measurements to be certain? Give a physical interpretation of this condition.