- #1

Benindelft

- 12

- 0

**[SOLVED] Fermi Dirac- missing something from Ashcroft derivation**

## Homework Statement

Deriving Fermi Dirac function

following ashcroft all good up to equation 2.43 but then it does the folowing at 2.44

and I can't see how you reach 2.44.

## Homework Equations

as

(2.43) f_{i}^{N}= 1- sum(P_{N}(E_{alpha}^{N+1}-E_{i}) which is 'summation over all (N+1) electron states alpha in which there is an electron in the one electron level i)

Then because

P_{N} (E)= exp(-(E-F_{N})/kT)

We may write

(2.44) P_{N}(E_{alpha}^{N+1}- E_{i})=exp((E_{i}-u)/kt)P_{N+1}(E_{alpha}^{N+1})

as u=F_{N+1}-F_{N}

## The Attempt at a Solution

I tried just subbing in but I am missing some important point and end up with rubbish....