Density of states free electron gas

[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?

 

[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

 

[nasu]

I thought that the proof is in an article by a guy named W. Ledermann, published in 1944.

http://rspa.royalsocietypublishing.org/content/182/991/362.full.pdf

I actualy found it mentioned in a review paper from 1993:
http://www.jstor.org/discover/10.2307/52288?uid=3739728&uid=2&uid=4&uid=3739256&sid=21102824926163

Do you know something about Sommerfeld writing something along the same lines?

 

[DrDu]

I think Ashcroft Mermin may mention the theorem.

 

[nasu]

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