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

(e)6 pts) Calculate the vectorrepresents the expectation value of the operatorat the time t. Plot the three components of this vector as functions of time.