Posted by Steve Simon on February 5, 2013, 4:35 pm, in reply to "Re: Phonons as bosons"
You could also think of these phonons as particles that can be inserted into orbitals. There is some orbital for wavevector k (orbital = e^{ikr}) and you insert n phonons into this orbital.
Part of the confusion is that there are two things that you can think of as being the "wavefunction". There is e^{i k r}, which is the orbital, and there is the amplitude of oscillation, which is the thing that is being quantized into eigenstates.
If you think about a single simple harmonic oscillator, you have a wavefunctions psi_n(x) where x is the displacement from equilibrium. For phonons, the "displacement from equilibrium" is actually the amplitude of the normal mode.
The number of phonons in the mode determines the (quantized) amplitude of oscillation of that mode.
Does that help at all?
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