申論題

15. (20 pts) Consider the spin state of a proton. Recall that the spin operators arewhere i =. Suppose that a static external magnetic field is applied along the y direction, so that the hamiltonian is where B is the magnetic field strength, and is a real constant. Denote the spin up state a and the spin down stateβ as

(d) (6 pts) T'he tine evolution of the spin state (t) obeys the time-dependent Schrodinger equation Together with the initial condition  (t = 0) given above, solve  (t).