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In introduction class to quantum mechanics, the example of the photoelectric effect is often shown to the students to explain how the classical physics fails to explain it. 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.

EDIT: If I understood it well, the weird thing in the photoelectric effect is that even at very high intensity (classically proportional to energy squared) the light can't overcome the work function if the light has a frequency which is too low. So my question is rather : How can one see that light is quantised and that the energy of a quanta depends on its frequency using quantum mechanics?

In introduction class to quantum mechanics, the example of the photoelectric effect is often shown to the students to explain how the classical physics fails to explain it. 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.

EDIT: If I understood it well, the weird thing in the photoelectric effect is that even at very high intensity (classically proportional to energy squared) the light can't overcome the work function if the light has a frequency which is too low. So my question is rather : How can one see that light is quantised and that the energy of a quanta depends on its frequency using quantum mechanics?

In introduction class to quantum mechanics, the example of the photoelectric effect is often shown to the students to explain how the classical physics fails to explain it. 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.

In introduction class to quantum mechanics, the example of the photoelectric effect is often shown to the students to explain how the classical physics fails to explain it. 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.

EDIT: If I understood it well, the weird thing in the photoelectric effect is that even at very high intensity (classically proportional to energy squared) the light can't overcome the work function if the light has a frequency which is too low. So my question is rather : How can one see that light is quantised and that the energy of a quanta depends on its frequency using quantum mechanics?