# Density of states free electron gas

1. Oct 24, 2013

### aaaa202

For a free electron gas the procedure for determining the density of states is as follows.
Apply periodic boundary conditions to the free electron waves over a cube of side L. This gives us that there is one state per volume 2$\pi$/L3=2$\pi$/V
And from there we can find the number of states at a given energy E by multiplying by the volume of a sphere at E in k space.
One big problem with this is however: Why do we assume that material is necessarily a cube? What if we worked with a ball of metal?

2. Oct 24, 2013

### DrDu

There is a theorem, I think by Sommerfeld, that the boundary becomes unimportant in determining e.g. the DOS in the limit V->infinity

3. Oct 24, 2013

### nasu

4. Oct 24, 2013

### DrDu

I think Ashcroft Mermin may mention the theorem.

5. Oct 24, 2013

### nasu

I am pretty sure they do. But who is the first to come with it?
I'll check the book.