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In chapter 10 of Kittel's "Introduction to Solid State Physics" it is said that the zeros of the dielectric functions determine the frequency of the longitudinal modes of oscillation, [tex]\epsilon(\omega_L) = 0[/tex], Eq. (17).

Am I missing something or this is actually an "unproved claim" as far as Kittel's book is concerned?

I mean, just below Eq (17), at page 276, there is a very short reference to depolarization, "to be discussed below". As far as I understand such a discussion is in the section "screening and phonons in metals" (page 286), where Eq. (17) is given for granted...

Hence, in summary, [tex]\epsilon(\omega_L) = 0[/tex] seems to me just a piece of information that Kittel gives us, without proving it. Or is it too obvious for proving?

Maybe I'm missing something... Sometimes one misses evident points when looking from a too short distance...

Has anyone any illuminating comment?

I have taken a look at more advanced textbooks, and, as far as I understand, it is a matter of poles and resonances..

Thanks a lot

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# Longitudinal acoustic phonons: why does the dielectric function vanish?

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