I am a bit puzzled by section 9.3 of the textbook, in which the argument that phonons are bosons is explained by saying that increasing the quantum number n means that multiple phonons may have the same wavevector quantum number k. But doesn't changing the value of n make the eigenstates distinct? I.e. if one phonon of wave vector k can fit in the n=0 state, and one in the n=1 state, this surely does not indicate degeneracy in a particular state (so does not provide evidence that phonons are bosons). Could you please tell me where I've gone wrong? Many thanks!
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