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For example, in the MIT online lecture notes for a course on elementary QM we find a statement about the historical development of the quantum theory that says that Einstein was able to explain the photoelectric effect by assuming the reality of the 'quanta' that Planck had used to come up with the solution to the ultraviolet catastrophe. The hyperphysics site says pretty much the same thing.

On the other hand, I occasionally read claims that the photoelectric effect in fact only demonstrates the quantum behavior of the electrons and that a classical treatment of the EM field is sufficient to yield the observed experimental details. While I'm in no mood to wade into the maths myself on this one, maybe there's someone on this forum who's already thought this through? I have a hard time believing that all of the introductory texts are both historically and physically incorrect. On the other hand, I've got this paper from 1968 that I keep meaning to work though that seems pretty legit. (The problem with being mathematically lazy is that you find yourself having to evaluate competing arguments from authority all of the damn time!)

I suspect the answer is that the classical treatment kind of works in limited cases but the quantized field is needed to make sense generally. Is this correct?