The analytical linear tetrahedron method?

[PRB147]

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.

 

[Jonath]

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

 

[PRB147]

@Jonath Thank you very much for your reply. I will reconsider the problem according to your suggestion

 

[PRB147]

Need further suggestions and hints

 

[PRB147]

I finally understand, I am so stupid and ridiculous.