Register to reply

Density of states free electron gas

by aaaa202
Tags: density, electron, free, states
Share this thread:
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?
Phys.Org News Partner Physics news on Phys.org
New complex oxides could advance memory devices
'Squid skin' metamaterials project yields vivid color display
Scientists control surface tension to manipulate liquid metals (w/ Video)
DrDu
#2
Oct24-13, 05:36 AM
Sci Advisor
P: 3,632
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: 1,988
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: 3,632
Density of states free electron gas

I think Ashcroft Mermin may mention the theorem.
nasu
#5
Oct24-13, 09:39 AM
P: 1,988
I am pretty sure they do. But who is the first to come with it?
I'll check the book.


Register to reply

Related Discussions
Significance of free electron gas density of states in different dimensions? Atomic, Solid State, Comp. Physics 12
Density of states for a free electron Advanced Physics Homework 3
Free Electron Density of States question Quantum Physics 2
The nearly free electron model and states in a band? Advanced Physics Homework 0
Density of states in 3d electron gas Advanced Physics Homework 2