Phonon density of states and density of states of free electrons

Click For Summary

Homework Help Overview

The discussion revolves around calculating the density of states (DOS) for free electrons and phonons, focusing on the differences in their representations in terms of energy and frequency. The original poster attempts to clarify the appropriate form for the phonon DOS in relation to the homework requirement of comparing two DOS.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster discusses their findings regarding the DOS for free electrons in different dimensions and questions the validity of their phonon DOS calculations. They seek clarification on whether the phonon DOS can be expressed in terms of energy and how to derive it if so.

Discussion Status

Some participants suggest consulting established texts for further understanding of phonon DOS and its relationship to dispersion relations. The conversation indicates that multiple interpretations of the problem are being explored, particularly regarding the representation of phonon DOS.

Contextual Notes

The original poster expresses uncertainty about the requirements of the homework, specifically whether to use energy or frequency for phonon DOS, indicating a potential gap in their understanding of the topic.

chikchok
Messages
7
Reaction score
0
Homework Statement
Compare phonon DOS and DOS of free electrons in 1D and 2D
Relevant Equations
D(E)1d=(1/L)dN/dE
D(E)2d=1/A)dN/dE for electrons
In the following pdf I tried to calculate the density of states of free electrons and phonons. First, I found the free electron DOS in 1D, it turns to be proportional to (energy)^(-1/2) and in 2D it is constant. However, I am not sure I found the DOS for phonons in the second part of the solution. Because the homework said to compare two DOS, I thought phonon DOS needs to be in terms of energy D(E) and not frequency w D(w). But I suspect it is wrong. Can phonon density of states be in terms of energy? If so, how to find it? And if not, should I find it trough equation D(w)dw?
 

Attachments

Physics news on Phys.org
This is a pretty broad question and I would suggest looking at Kittel or Ashcroft and Mermin for the phonon part. I believe the question wants you to see that the dispersion relation for phonons can resemble that of photons. There is a lot of good physics in this question and it is worth some effort.
 
I`ve looked up the DOS of a phonon in Kittel`s book and in 1D DOS is 1/pi*vg (vg as a group velocity dw/dk) and in 2D it`s k/2pivg . Both of them have no relationship with energy. That is why I was wondering if there is a way to calculate the DOS as a function of energy.
 
$$E=\hbar \omega$$
 
Reply
  • Like
Likes   Reactions: docnet

Similar threads

Graduate Phonon Density of States (PDOS) at Gamma Point
  • · Replies 1 ·
Replies
1
Views
3K
Physical explanation of energy shift in Heisenberg term in t-J model
  • · Replies 3 ·
Replies
3
Views
3K
Express entropy density in terms of energy density (Ashcroft/Mermin)
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Density of States: 1-Dim Linear Phonons & Electrons Differences
  • · Replies 4 ·
Replies
4
Views
2K
Dependence of Hall coefficient on temperature in semiconductors
  • · Replies 1 ·
Replies
1
Views
2K
What factors affect the mean free path of phonons in Germanium at 300K?
  • · Replies 1 ·
Replies
1
Views
3K
Density of states, and integral of the Sommerfeld type
  • · Replies 6 ·
Replies
6
Views
3K
How Does the Density of States Apply to Electrons in Bands?
  • · Replies 3 ·
Replies
3
Views
2K
Density of states for a free electron
  • · Replies 3 ·
Replies
3
Views
4K
Graduate Are there phonons in a free electron gas?
  • · Replies 7 ·
Replies
7
Views
3K