I am trying to solve this. But I got confused in part b because the particle is now in the up state so I was wondering what effect a magnetic field will have on the state? In other words, will the past state have an effect or I just compute the Hamiltonian and write the new state as a superposition of stationary states without any reference to its past state?
Consider a spin 1=2 particle. At time t = 0, the particle is in the state |+>
(a) At time t = 0, we measure Sx and find a value 1/2 h bar. What is the state vector immediately after the measurement?
(b) At the same instant of the measurement, we apply a constant magnetic field B = B_0k ^ on the particle and allow the particle to precess for a time T. What is the state of the system at t = T?
(c) At t = T, the magnetic field is very rapidly rotated so that it is now B = B_0^ j. After another time interval T, a measurement of Sx is carried out once more. What is the probability that a value 1/2 h bar is found?