Band structure and dispersion relations

Click For Summary
SUMMARY

This discussion focuses on the calculation of band structure for a Fermi gas under a harmonic potential, contrasting it with a Bose gas. The partition function for both gases is expressed, highlighting the distinction between bosons and fermions through the constant "b". The user seeks clarification on whether band structure and dispersion relations are equivalent concepts and requests methods for calculating band structure, referencing "Ashcroft: Solid State" for potential methodologies. The conversation emphasizes the importance of understanding the energy spectrum and density of states, specifically for fermionic systems.

PREREQUISITES
  • Understanding of Fermi and Bose gases
  • Knowledge of partition functions in statistical mechanics
  • Familiarity with band structure concepts in solid-state physics
  • Basic grasp of harmonic potentials and their implications
NEXT STEPS
  • Study the methods for calculating band structure in "Ashcroft: Solid State"
  • Learn about the relationship between dispersion relations and energy spectra
  • Explore the derivation of density of states n(e) for fermionic systems
  • Investigate differential equations relevant to ω(k) in fermionic cases
USEFUL FOR

Physicists, materials scientists, and students studying solid-state physics, particularly those interested in the properties of fermionic and bosonic systems under harmonic potentials.

lokofer
Messages
104
Reaction score
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.

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

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 \omega (k) in the "Fermionic" case?..thanks.
 
Last edited:
Physics news on Phys.org
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.
 

Similar threads

Graduate Electronic band structure of iron superconductor BaFe2As2
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Relation between electronic band structure and Fermi energy
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Mastering DFT: Calculating Band Structures for Heterostructures
  • · Replies 2 ·
Replies
2
Views
4K
Graduate Conductance of an interacting quasi one dimensional wire
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Band Structure of a solid is not related to the size/doping?
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Band structure and valence electrons
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Problem about electronic structure
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Why is CNT considered a 1D structure despite having movement in two dimensions?
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Empirical tight-binding sp3s* band structure of semiconductors
  • · Replies 2 ·
Replies
2
Views
2K
Graduate How Can We Calculate Band Bending Using Schrödinger-Poisson Theory?
  • · Replies 3 ·
Replies
3
Views
2K