Question about the total number of states in Sommerfeld model

Physics Q&A
1

Dear Solid State group,

I have a question about the following equation for the total number of states in the chapter about the Sommefeld model:

Screenshot from 2021-05-06 14-21-26
Screenshot from 2021-05-06 14-21-26532×162 6.26 KB

Is this factor 2_s in front of the equation right? I mean, there are two electrons per energy state, so this equation would not give the total number of electrons in the system?

Yours Faithfully,

2

Hey, @lucas.bandeira, that factor is counting the spin degeneracy. Naturally, it’s only there if the spins are degenerate, and if we don’t already include this factor in \int_{\varepsilon(\mathbf{k})<\varepsilon}d\mathbf{k}.

Hope that helps.