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Density of states free electron gas

by aaaa202
Tags: density, electron, free, states
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aaaa202
#1
Oct24-13, 04:23 AM
P: 1,005
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[itex]\pi[/itex]/L3=2[itex]\pi[/itex]/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?
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DrDu
#2
Oct24-13, 05:36 AM
Sci Advisor
P: 3,593
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
#3
Oct24-13, 09:32 AM
P: 1,969
I thought that the proof is in an article by a guy named W. Ledermann, published in 1944.

http://rspa.royalsocietypublishing.o...1/362.full.pdf

I actualy found it mentioned in a review paper from 1993:
http://www.jstor.org/discover/10.230...21102824926163

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

DrDu
#4
Oct24-13, 09:38 AM
Sci Advisor
P: 3,593
Density of states free electron gas

I think Ashcroft Mermin may mention the theorem.
nasu
#5
Oct24-13, 09:39 AM
P: 1,969
I am pretty sure they do. But who is the first to come with it?
I'll check the book.


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