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Density of states free electron gas 
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#1
Oct2413, 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]/L^{3}=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? 


#2
Oct2413, 05:36 AM

Sci Advisor
P: 3,571

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
Oct2413, 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? 


#4
Oct2413, 09:38 AM

Sci Advisor
P: 3,571

Density of states free electron gas
I think Ashcroft Mermin may mention the theorem.



#5
Oct2413, 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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