A particle of mass m and charge e oscillates in a one-dimensional harmonic potential with angular frequency ω.
(a) Show, using perturbation theory, that the effect of an applied uniform electric field \mathbf{E} is to lower all the energy levels by e^{2}|\mathbf{E} |^{2} /2m\omega^{2}.
(b) Compare this with the classical result.
(c) Use perturbation theory to calculate the new ground-state wave function.