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Energy band calculations for a perfect crystal and a crystal with impurities using a nonlocal potential model
Author(s) -
Fock H.
Publication year - 1971
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.2220470223
Subject(s) - eigenfunction , impurity , lattice (music) , physics , band gap , electron , electronic band structure , crystal (programming language) , condensed matter physics , quantum mechanics , atomic physics , eigenvalues and eigenvectors , computer science , acoustics , programming language
The local potential at each lattice site is replaced by a nonlocal projection operator. Then the eigenfunctions of the electrons can simply be canceled out from the Schrödinger equation. The method of Green's functions is utilized and the calculation of the energy band is restricted to a simple cubic lattice and s‐symmetrical potential function. Energy levels for point impurities and energy bands for one‐ and two‐dimensional impurities are obtained within the band gap or under the valence band. This depends on the depth and the range of the perturbing potential.