A free electron is at rest in an oscillating magnetic field pointing in the z-direction: B(t) a constant. The interaction Hamiltonian is given by: Bo cos(wt)k, where Bo is e§. B(t) H = - m (a) If at time t=0, the electron is in a state with spin up in the x-direction, find the probability that at a later time t=T, the electron will be in a state with spin down in x-direction, i.e. (S½) = –. (b) Find an expression for the minimum value of the magnitude of the magnetic field, Bo, that will result in a complete spin flip.

A free electron is at rest in an oscillating magnetic field pointing in the z-direction: B(t) a constant. The interaction Hamiltonian is given by: Bo cos(wt)k, where Bo is e§. B(t) H = - m (a) If at time t=0, the electron is in a state with spin up in the x-direction, find the probability that at a later time t=T, the electron will be in a state with spin down in x-direction, i.e. (S½) = –. (b) Find an expression for the minimum value of the magnitude of the magnetic field, Bo, that will result in a complete spin flip.