There is a mistake in the lecture notes of the tight binding model, with the derivation of g(E). There is a hbar present, but I think it is not supposed to be there. Could you maybe give it a look?
Hey there, thanks for the feedback. However, it seems the notes are correct. The \hbar comes from using the definition of velocity v = \frac{1}{\hbar}\frac{d E}{dk}
edit: although the given definition of velocity is indeed faulty later down below.
I believe in the initial expression for g(E), there should be a factor 1/hbar instead of hbar.
In the expression for |v|^-1, there should be a factor hbar.
Then those 2 cancel in the final expression for g(E).
Where would the initial 1/\hbar be coming from in g(E)? The expression looks correct to me. It has the L/2 \pi which is the k space density and then dk/dE which is the number of states per energy interval.
|dk/dE| = \frac{1}{\hbar}|v|^{-1}
Ah, good eye! Thanks for pointing that out. Indeed, the \hbar should go below and then cancel out later down the road.