Consider a charged particle in the one-dimensional harmonic oscil- lator potential. suppose we turn on a weak electric field (e) so that the potential energy is shifted by an amount h' -qex (a) show that there is no first-order change in the energy levels, and calculate the second-order correction. hint: see problem 3.50. (b) the schrödinger equation can be solved exactly in this case by a change of variables: xx-(qe/mw2). find the exact energies, and show that they are consistent with the perturbation theory approximation