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2) Regarding the Thomas-Fermi approximation, in my textbook (Kittel) it says that it is valid for electron wavenumbers much smaller than the fermi wavevector - so larger wavelengths than the fermi wavelength. If I am looking at impurity scattering in a metal, then surely you cannot apply the TF approximation since the electrons will all be at the Fermi level and so the wavenumber of the scattered electrons will equal that of the fermi wavevector. However I have seen the TF used for graphene particularly, so how is that a valid assumption?

Cheers.