Density of states free electron gas

In summary, the procedure for determining the density of states for a free electron gas involves applying periodic boundary conditions to free electron waves over a cube of side L. This results in one state per volume 2π/L^3 = 2π/V. To find the number of states at a given energy E, one can multiply by the volume of a sphere at E in k space. However, this method assumes that the material is a cube, which may not always be the case. There is a theorem by Sommerfeld that states the boundary becomes unimportant in determining the density of states as the volume approaches infinity. This theorem was proven by W. Ledermann in 1944 and has been mentioned in various articles and books, including the
  • #1
aaaa202
1,169
2
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?
 
Physics news on Phys.org
  • #2
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
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?
 
  • #4
I think Ashcroft Mermin may mention the theorem.
 
  • #5
I am pretty sure they do. But who is the first to come with it?
I'll check the book.
 

1. What is the definition of "density of states" for a free electron gas?

The density of states for a free electron gas is a measure of the number of available energy states per unit volume for a given energy range. It represents the amount of energy levels that are accessible to electrons in a material.

2. How is the density of states for a free electron gas calculated?

The density of states for a free electron gas is calculated by dividing the energy range by the energy spacing between each level. This results in the number of energy levels per unit volume. It can also be calculated using mathematical equations based on the energy levels of the system.

3. What factors affect the density of states for a free electron gas?

The density of states for a free electron gas is affected by several factors, including the material's band structure, temperature, and external magnetic or electric fields. These factors can change the energy levels and spacing between them, thus altering the density of states.

4. Why is the density of states important in materials science?

The density of states is an essential concept in materials science because it helps us understand the electronic properties of materials. It provides information about the number of energy levels available for electrons to occupy, which affects the electrical conductivity, thermal conductivity, and other properties of a material.

5. How does the density of states differ between a metal and an insulator?

The density of states for a metal is continuous, meaning there are many available energy levels for electrons to occupy. In contrast, the density of states for an insulator is discrete, with a large energy gap between levels that are not accessible to electrons. This difference in the density of states is what makes metals good conductors and insulators poor conductors of electricity.

Similar threads

Replies
1
Views
1K
  • Atomic and Condensed Matter
Replies
0
Views
392
  • Atomic and Condensed Matter
Replies
5
Views
1K
  • Atomic and Condensed Matter
Replies
7
Views
1K
  • Atomic and Condensed Matter
Replies
4
Views
2K
  • Atomic and Condensed Matter
Replies
1
Views
2K
  • Atomic and Condensed Matter
Replies
6
Views
1K
  • Advanced Physics Homework Help
Replies
3
Views
1K
  • Quantum Physics
Replies
16
Views
1K
  • Atomic and Condensed Matter
Replies
4
Views
3K
Back
Top