# Homework Help: I need help solving an integral over density of states for electrons.

1. Aug 9, 2011

### mattek1979

1. The problem statement, all variables and given/known data
I am trying to retake an old course in statistical mechanics but run into integrals that i simply have forgotten how to solve.

Given an denstiry of states such that
$f(\epsilon)= \frac{1}{|\epsilon |}$ for $\epsilon_{min} \leq \epsilon < 0$ and 0 elsewhere

Using the mean occupation number for a fermi-dirac distribution, I am supposed to find the fermi energy for N electrons.

2. Relevant equations

I assume integrating

$dN(\epsilon)=\bar{n}(\epsilon)f(\epsilon)d\epsilon$

using
$\bar{n }=\frac{1}{e^{-\beta(\epsilon-\mu)}+1}$

and the above

$f(\epsilon)=\frac{1}{|\epsilon|}$
is the way to proceed.

3. The attempt at a solution

The integral I seek to solve is

N=$\int^{\epsilon_{min}}_{0}\frac{1}{|\epsilon|}\frac{1}{e^{-\beta(\epsilon-\mu)}+1}d\epsilon$

and I simply can't figure out if I need to do a subtitution of integration variables or if i am missing some other nifty technique.

All help appreciated

Sincerely
Mathias Kristoffersson

Last edited: Aug 9, 2011
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