We know that the Bloch theorem about electrons in a perfect crystal help us to investigate desired properties of solids.
So as we know, because of the periodicity of the lattice, we use the Fourier series (for periodic and non-periodic) to go to the wave-vector space.
as far as I know, we can use the Fourier transform (for periodic and non-periodic functions) to go to the wave-vector space. But, why don't we do this and use the Fourier series? (What are the limitations that prohibit us of doing FT?)
Why not using FT in this problem?