- #1

RicardoMP

- 49

- 2

Hi!

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.

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.