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Incompletely symmetric non‐bloch electron states in perfect cubic crystals. I. Eigenproblem and its solution
Author(s) -
Kunert A.
Publication year - 1978
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560140202
Subject(s) - irreducible representation , wave function , cubic crystal system , bessel function , point group , bravais lattice , bloch wave , lattice (music) , quantum mechanics , spherical harmonics , mathematics , mathematical analysis , physics , condensed matter physics , crystal structure , chemistry , geometry , crystallography , acoustics
In the studies on impure metals where the perturbation potential due to the impurity has symmetry of the point group of the crystal, subdivision of the electron density of the pure metal into irreducible representations of the point group is of significance. A method is presented for the calculation of wave functions of the perfect cubic crystal which transform according to the incompletely symmetric irreducible representations of the point group. The functions were evaluated in the LCAO approximation using s ‐type AOS for the face centered cubic lattice. These are in the form of standing waves, and their coefficient functions are linear combinations of the products of the cubic harmonics of a suitable type and the spherical Bessel functions. Properties of the solutions obtained were examined. Numerical calculations were made for four irreducible representations of the point group.