A particle starts out (at time t = 0) in the N th state of the infinite square well. Now the "floor" of the well rises temporarily (maybe water leaks in, and then drains out again), so that the potential inside is unifonn but time dependent: Vo(t ), with Vo(O) = Vo( T) = 0.
(a) Solve for the exact t111 (t), usi ng Equation 9.82, and show that the wave function changes phase, bu t no transitions occur. Find the phase change, (T) , in tenns of the function Vo(t).
(b) Analyze the same problem in first-order perturbat ion theory, and compare your answers.