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Approximation of Electron Energy Bands by Cubic Splines
Author(s) -
Neumann J.,
Smrčka L.
Publication year - 1987
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.2221410215
Subject(s) - brillouin zone , hermite polynomials , monotone cubic interpolation , cubic hermite spline , eigenvalues and eigenvectors , cube (algebra) , symmetry (geometry) , mathematics , electron , mathematical analysis , physics , second derivative , quantum mechanics , geometry , bicubic interpolation , polynomial , linear interpolation
Cubic spline functions are used to interpolate between the band energy eigenvalues evaluated on the regular cubic mesh of points in the irreducible part of the Brillouin zone (IBZ) making use of the knowledge of normal gradients of eigenenergies at the IBZ faces following from the crystal symmetry. The resulting approximate function has the full symmetry of the energy band and is represented within each cube by three‐dimensional Hermite splines which join together smoothly with continuity up to second derivative accross the cubes boundaries.