So when the phonon energy increases, the reason it does so incrementally (i.e., quantized) is because the vibrational modes of the crystal have disrcrete energies? Or is it because the number of oscillators (molecules) is increasing by one, additional individual oscillators thus adding their...
I did look at the wiki article, thanks. I found it to be mathematically consistent with texts, but I didn't find the physical sense I'm trying to get. It gives a visual representation of the propagation of sound, but not quantization as far as I can tell.
If the fact that the lattice is made of particles explains sound quantization, then does that imply that phonons could have been discovered prior to the advent of the Schrodinger equation?
I'm looking for some physical intuition as to why sound waves are quantized.
I know two mathematical procedures for deriving phonons in a lattice: 1) impose the canonical commutation relations on the system ad-hoc, and 2) apply the Schrodinger equation to the lattice. But neither of these...