Band structure and dispersion relations

  • Thread starter lokofer
  • Start date
  • #1
106
0
-Let's suppose we have 2 gases ..one is a "Fermi" gas under an Harmonic potential and the other is a "Bose" gas under another Harmonic potential... in both cases (as an approximation) the particles (bosons and electrons are Non-interacting) then we could write the partition functions.

[tex] \prod _{k=1}^{\infty}(1+be^{\beta \omega (k)})^{-1} [/tex]

Where "b" is a constant equal to 1 (electrons) or -1 (bosons)..my question is HOw could we calculate the "band structure" for the Fermion gas... ¿are the band structure and dispersion relations the "same" concept but one is valid for Bosons and other for Fermions?.. I've read "Ashcroft: Solid State..." where you can find lot's of method to calculate band structure..but what's the best?.., Is there a differential equation or other type of equation satisfied for the [tex] \omega (k) [/tex] in the "Fermionic" case?..thanks.
 
Last edited:

Answers and Replies

  • #2
76
0
calculate n(e) i.e the density of states. You keep referring to a dispersion relation, and this euphimism of dispersion relation for w(k). you already know what w(k) is if you know the partition function and hence the energy spectrum. i think you are getting confused with terminogy here as you have presented the same question before and it does not make sense.
 

Related Threads on Band structure and dispersion relations

Replies
8
Views
5K
Replies
1
Views
1K
  • Last Post
Replies
6
Views
4K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
5
Views
6K
  • Last Post
Replies
5
Views
4K
Replies
4
Views
1K
Replies
11
Views
2K
  • Last Post
Replies
1
Views
2K
Replies
4
Views
804
Top