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Interpolation of the One‐Electron Energies Using Theoretical‐Numerical Nets
Author(s) -
Kanalin A. G.,
Mokhracheva L. P.
Publication year - 1991
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221640118
Subject(s) - interpolation (computer graphics) , fourier series , mathematics , series (stratigraphy) , brillouin zone , trigonometric interpolation , mathematical analysis , quadratic equation , piecewise , linear interpolation , fourier transform , convergence (economics) , polynomial interpolation , physics , polynomial , geometry , quantum mechanics , classical mechanics , motion (physics) , paleontology , economics , biology , economic growth
The method of global Fourier‐series approximation of the one‐electron energies ϵ( k ) in the Brillouin zone is considered. To calculate the Fourier series expansions of the ϵ( k )‐functions optimal for trigonometric polynomials theoretical‐numerical nets are used. Convergence and accuracy of the approximation is investigated using one‐ and two‐band models of the ϵ( k )‐dependence. It is shown that the method described is more accurate then piecewise linear interpolation in the volumes of elementary tetrahedra, generated in regular nets, and is comparable to piecewise quadratic interpolation.