The analytical linear tetrahedron method?

In summary, the conversation discusses the work of G. Lehmann and M. Taut on the calculation of the density of states and related properties. The question being addressed is how the middle line of Eq. (3.9) is derived, specifically why f(ε) is equal to f0-f1. The conversation also mentions the importance of the function of energy being positive and how it can be verified through experimental and theoretical formulations. Finally, the individual expresses gratitude for the suggestion given by Jonath and admits to understanding the problem after further consideration.
  • #1
PRB147
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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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  • #2
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
 
  • #3
@Jonath Thank you very much for your reply. I will reconsider the problem according to your suggestion
 
  • #4
Need further suggestions and hints
 
  • #5
I finally understand, I am so stupid and ridiculous.
 

1. What is the analytical linear tetrahedron method?

The analytical linear tetrahedron method is a mathematical technique used in scientific research to analyze and model the relationships between multiple variables. It involves constructing a tetrahedron (a triangular pyramid) with each of the four vertices representing a variable, and using mathematical equations to calculate the relationships between the variables.

2. What are the advantages of using the analytical linear tetrahedron method?

One of the main advantages of this method is its ability to visualize and understand complex relationships between multiple variables. It also allows for the identification of important variables and their impact on the overall system. Additionally, the method is relatively simple and can be used for both linear and nonlinear relationships.

3. How is the analytical linear tetrahedron method different from other statistical methods?

The analytical linear tetrahedron method differs from other statistical methods in that it focuses on visualizing and analyzing relationships between multiple variables rather than just analyzing the relationship between two variables. It also allows for the incorporation of nonlinear relationships, which is not possible with some other statistical methods.

4. What types of data are suitable for the analytical linear tetrahedron method?

The analytical linear tetrahedron method can be used with any type of data, including numerical, categorical, and ordinal data. It is also suitable for both continuous and discrete data. However, the accuracy and effectiveness of the method may vary depending on the nature and quality of the data.

5. How is the analytical linear tetrahedron method used in scientific research?

The analytical linear tetrahedron method is primarily used in scientific research to analyze and model complex relationships between multiple variables. It can be applied in various fields such as biology, chemistry, physics, economics, and social sciences. It is also commonly used in data analysis and predictive modeling to understand and predict the behavior of a system.

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