In introduction class to quantum mechanics, the examples of the photoelectric effect is often shown to the students to explain how the classical physics fails to explain them. We are told that one can solve the problem by only allowing the light to have discrete energies, proportional to the frequency of the light.

But somehow I can't see what is the connexion between these discrete energies of the photons and the rest of the stuff we learn (wave function, Schrödinger equation). Is it possible to predict the photoelectric effect using Schrödinger's equation on a wave function? If this is the case, I would be very happy to know how.