I have a question about QM, which perhaps somebody here can answer: Is quantization an inherent property of the photon, or is it a property of the material (or of the interaction with it)?
Einstein wrote the equation "E = h*(nu)", where h is the so-called "Planck's constant", and nu is the frequency of light. Translated, this means that each photon carries an amount of energy proportional to its frequency, higher-frequency photons (IR -> red -> blue -> UV -> X-ray) carry more energy.
tl;dr: Quantization is an inherent property of light.
The quantization of light shows up in how it interacts with particles -- even unbound particles like free electrons, which also do not have quantized energy levels. Specifically, if light were NOT quantized, you could get the same effect with more intense light that you get with more energetic light. Instead, experiments show again and again that longer-wavelength light at high intensity gives a totally different effect from short-wavelength light at low intensity. Postulating that light consists of particles (photons) with E = h(nu) explains this difference.
Yes, but the question is whether that is due to the material not being able to produce non-quantized photons. Stated differently, suppose we had a different way of generating photons, then could we theoretically create them in a non-quantized way?
The quantised states are the different solutions to that equation (the different energy levels + spin states in an atom.) - this holds for electrons in atoms being quantised.
The photoelectric effect, which has to do with incident photons, showed that you can't turn up the intensity of long wavelength light and ping electrons off things: the power input didn't change things, but a very low power of short wavelength photons did. Thus, Einstein concluded that there must be something specific about the energy of individual particles, not just the total energy stored in a wave. So it is observed in an interaction, but the information defining the final effect travels with the photon.