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Calculation of Dipole Transition Matrix Elements in Muffin‐Tin Models
Author(s) -
Shilkova N. A.,
Shirokovskii V. P.
Publication year - 1988
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.2221460117
Subject(s) - tin , matrix (chemical analysis) , wave function , momentum (technical analysis) , position and momentum space , function (biology) , physics , dipole , surface (topology) , mathematical analysis , space (punctuation) , quantum mechanics , mathematics , geometry , chemistry , linguistics , philosophy , organic chemistry , finance , chromatography , evolutionary biology , economics , biology
Matrix elements of momentum and of gradient of the potential for electronic states in solids are calculated by the Green's function method. Their absolute identity is shown if the integral over the elementary cell volume is correctly reduced to integrals over the space restricted by the muffin‐tin sphere, and through the surface of this sphere. It is ascertained that the surface term gives the main contribution in momentum matrix element values. It is proved that the commutation relationship connecting both the types of matrix elements is exactly valid for the muffin‐tin function irrespective of the variational series length. The influence of high‐angular‐momentum terms in the expansion of the wave function on the matrix element values is discussed.