Consider a spin-1/2 particle with a magnetic moment. at time t = 0, the state of the particle is \\(t = 0)) = 1 +). a) if the observable sy is measured at time t = 0, what are the possible results and the probabilities of those results? b) instead of performing the above measurement, the system is allowed to evolve in a uniform magnetic field b = bog. calculate the state of the system (in the s, basis) after a time t. c) at time t, the observable sy is measured. what is the probability that a value h/2 will be found? d) draw a schematic diagram of the experiment in parts (b) and (c), similar to fig. 3.2.