1. A particle of mass m is prepared in the ground state of an infinitc potential box of size a extending from x=O to x=a. Suddenly, the wall at x=a is moved to x=2a with i n a time At doublin g the box size. Assume that the wavcfunction is the same immediately after the change, if the change happens fast enough.
(a) What is the physical meaning of "fast enough" in quantum mechanics?
(b) Determine the probability of finding the particle in the second (n=2) state of the new well, immediately after the change. Note that the wavelength within the well, and hence the energy, for this state is the same as for the initial state in the well before its expansion. Do not
forget to pro perly normalize the wave-functions for your calculations.
(c) What is the probability that the particle is found in the ground state after the sudden expansion?
(d) Calculate the expectation value of the energy of the particle before and after the sudden expansion?