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On the Calculation of the Narrow Band Width in Solids
Author(s) -
Perrot F.
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.2220460218
Subject(s) - bound state , radius , crystal (programming language) , physics , logarithm , function (biology) , angular momentum , logarithmic derivative , upper and lower bounds , electronic band structure , condensed matter physics , momentum (technical analysis) , mathematical analysis , quantum mechanics , mathematics , computer security , finance , evolutionary biology , computer science , economics , biology , programming language
Abstract Using the APW method for the crystal states description, an upper bound to the band width of the tight bound core states in solids can be obtained from the calculation of two particular solutions of the Schrödinger radial equation with respect to the crystal muffin‐tin potential and the dominant angular momentum in the band. An analytical expression of the dominant logarithmic derivative calculated as a function of energy at the APW sphere radius is then derived, which saves much computer time if different points in the band have to be exactly computed. A numerical test is performed on the 1s state in solid lithium.