Please help with the QM question below:

1,5Problem 2 - Simple Harmonic Oscillator in an Electric Field (10 points) Consider a charged particle, with charge q, in a simple harmonic oscillator potential with an applied electric field Ey. That is, let the Hamiltonian of the system be mu 2 H = + 2 2 qEji. (3) 2m 2 ? for ? (a) (4 points) Compute the energy levels of this system (hint: you can complete the square, e.g. something like A2 + ba = (A +Vox)2 - something). (b) (3 points) Compute the energy eigenfunctions In () of the system in terms of the energy eigenfunctions when the electric field is zero (E| = 0). Call the zero-electric-field energy eigenfunc- tions To (c) (3 points) Compute the commutators [H, x] and [H, p]