The analytical linear tetrahedron method?

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Discussion Overview

The discussion revolves around the analytical linear tetrahedron method, specifically focusing on the derivation of a particular equation related to the density of states in a physical system. Participants explore the theoretical underpinnings and implications of the function of energy.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant references the work of G. Lehmann and M. Taut, questioning the derivation of the equation f(ε)=f0-f1 and expressing an intuitive disagreement with it.
  • Another participant clarifies the range of energy values, suggesting that the order of energy must follow a specific sequence and that the function of energy must be positive, supporting the equation f(ε)=f0-f1 through experimental and theoretical formulations.
  • A participant expresses gratitude for a suggestion and indicates a willingness to reconsider their understanding of the problem.
  • Another participant requests further suggestions and hints to aid their understanding.
  • A later reply reflects a personal realization about their understanding of the topic, expressing feelings of inadequacy.

Areas of Agreement / Disagreement

Participants appear to have differing views on the validity of the equation f(ε)=f0-f1, with some supporting it based on energy conditions while others express skepticism. The discussion remains unresolved regarding the derivation and implications of this equation.

Contextual Notes

There are limitations in the discussion related to the assumptions underlying the function of energy and the specific conditions under which the equation is considered valid. The mathematical steps leading to the equation's derivation are not fully resolved.

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The pioneering work by G. Lehmann, M. Taut, please see the attached files or download from wiley
On the Numerical Calculation of the Density of States and Related Properties,
http://onlinelibrary.wiley.com/doi/10.1002/pssb.2220540211/abstract

The question is how the middle line of Eq. (3.9) can be derived?
i.e. why f(ε)=f0-f1

intuitively, it is wrong.




 

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From the second condition in the function of energy the range is clear that Δε1<=ε<=Δε2

Therefore, the order of energy becomes Δε0 <= Δε1 <= ε <= Δε2 <= Δε3

The function of the energy must be positive and by experimental and theoretical formulations the function of energy is given by

f(ε)=f0-f1

U can verify it by giving some positive energy values to Δε0, Δε1, ε, Δε2, Δε3 in the order of energy
 
@Jonath Thank you very much for your reply. I will reconsider the problem according to your suggestion
 
Need further suggestions and hints
 
I finally understand, I am so stupid and ridiculous.
 

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