A particle of mass m bounces vertically between a hard floor at z=0 and a hard ceiling at z=L, with no gravity (g=0) inside.
(a) Write down the energy eigenvalues and eigenfunctions.
(b) Now add a small gravitational perturbation V′=mgz. Use first-order perturbation theory to find the corrected energy levels En(1).
(c) In which limit does the perturbative approach break down, and what controls this?