Phonons are quantized lattice vibrations. They are travelling waves of the form exp(ikr) taken to satisfy periodic boundary conditions. I'm guessing periodic boundary conditions are equivalent to demanding the waves to be zero at the boundary. which is what characterizes standing waves (right? :S) So are all phonons really just the number of possible standing waves you can form from the solutions exp(ikr). And if so, how is one to interpret phonon-phonon collisions? What happens physically when two standing wave vibrations collide and why can we speak of conservation of the crystal momentum?