3. Consider a spin 1/2 particle placed in a magnetic field Bo with components: B By B === == 0 1 Bo = The notation is the same as that of exercise (1). a. Calculate the matrix representing, in the (+), | -> } basis, the operator H, the Hamiltonian of the system. b. Calculate the eigenvalues and the eigenvectors of H. c. The system at time = 0 is in the state | ->. What values can be found if the energy is measured, and with what probabilities? d. Calculate the state vector 14 (1)) at time t. At this instant, S, is measured; what is the mean value of the results that can be obtained? Give a geometrical interpretation.