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Quasi‐Classical Quantization for Potentials with an Infinite Surface Barrier. Subbands in Inversion Layers
Author(s) -
Paasch G.,
Fiedler T.,
Klář M.,
Bartoš I.
Publication year - 1983
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.2221180221
Subject(s) - wkb approximation , quantization (signal processing) , eigenvalues and eigenvectors , inversion (geology) , density of states , rectangular potential barrier , surface states , ground state , surface (topology) , mathematics , physics , quantum mechanics , mathematical analysis , geometry , biology , paleontology , algorithm , structural basin
For potentials with a high surface barrier, quasi‐classical quantization schemes are investigated. WKB and other previous approximations provide good results for the lower eigenvalues in special cases only. Here a modified local density approximation is used for the calculation of the density of states. From the integral density of states a quantization expression is derived where the ground state constant depends explicitly on the shape of the potential. It yields the whole eigenvalue spectrum very precisely for quite different potentials with surface barrier. The application to subband energies in inversion layers is discussed.