Discuss the below:
Time dependent perturbation: electron spin problem
An electron is in a strong, uniform, constant magnetic field with magnitude B_0 aligned in the +x direction. The electron is initially in the state |+> with x component of spin equal to hbar/2. A weak, uniform, constant magnetic field of B_1 (where B_1 << B_0) in the +z direction is turned on at t=0 and turned off at t=t_0. Let P(i -> f) be the probability that the electron is in the state |-> with x component of spin equal to -hbar/2 at a later time t_f > t_0. Show that
P(i -> f) = (B_1/B_0)^2 sin^2(u_B B_0 t_0 /hbar)