Solution of Dirac Delta DOS Equation

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Discussion Overview

The discussion revolves around the solution of the Dirac delta function in the context of the density of states (DOS) equation, specifically focusing on its formulation and interpretation within solid state physics. The conversation includes technical aspects of the equation and its implications for energy bands.

Discussion Character

  • Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant presents the DOS equation involving the Dirac delta function and seeks clarification on its solution.
  • Another participant questions the validity of the expression, indicating potential confusion or missing elements.
  • A third participant suggests using LaTeX formatting for clarity and requests a clearer statement of the problem.
  • One participant describes the equation as representing the density of states at energy E from multiple bands, noting that the delta function filters the energy spectrum.
  • Another participant proposes a modified version of the equation and inquires about references supporting this solution.
  • A later reply suggests an alternative formulation of the DOS equation and references a well-known textbook in solid state physics for further reading.

Areas of Agreement / Disagreement

Participants express differing views on the formulation and interpretation of the DOS equation, with no consensus reached on the correct expression or solution. Multiple competing perspectives are presented.

Contextual Notes

Some participants indicate potential confusion regarding the expression, and there are references to established literature, suggesting that the discussion may depend on specific definitions and interpretations of the terms involved.

Who May Find This Useful

This discussion may be of interest to those studying solid state physics, particularly in understanding the density of states and the application of the Dirac delta function in energy band theory.

mahdi
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What is the solution of Dirac delta function of density of sate equation below:

DOS(E)=2/N ∑ ∫(1/dEj(k)/dk).δ[Ej(k)-E]dE
 
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are you sure this expression makes sense? Maybe I miss something?
 
mahdi said:
What is the solution of Dirac delta function of density of sate equation below:

DOS(E)=2/N ∑ ∫(1/dEj(k)/dk).δ[Ej(k)-E]dE

Hi,you can use " tex formula tex " to eidt your formula as follows

\frac{1}{2}Ax= b

and state your problem clearer.
 
Thank you, I'm attaching the equation in word denouement.
 

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This is basically the density of state at energy E from N_hex bands. The delta function filters out the energy spectrum at E_j(k_t)=E. 1/|dE/dk| gives density of state at E from the given band
 
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Do you mean the final equation become like this DOS(E)=E. 1/|dEj/dk|

please do you have a reference of this solution ?
 
should be DOS(E)= sum_j (1/|dEj/dk|). Take a look at Ashcroft and Mermin's solid state physics
 
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