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I'm trying to show how the chemical potential depends on the temperature and i'm advised to use the Sommerfeld expansion. I'm using it on the density of charge [tex] n=\int^{+\infty}_{-\infty} \rho(\epsilon)n_Fd\epsilon [/tex], which gives [tex] n=\int^{\mu}_{0} \rho(\epsilon)d\epsilon +\frac{\pi^2}{6}(k_BT)^2\frac{d\rho(\epsilon)}{d\epsilon}|_{E=\mu}[/tex].

After having a hard time trying to insert a term with a [tex] \mu [/tex] in it, I searched on google and found the following excerpt that I uploaded. I don't understand the second paragraph and how it gives the [tex] (\mu-E_F)\rho(\epsilon) [/tex] term.

Thank you for your time.

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# I Sommerfeld Expansion & Chemical Potential

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