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Multiresolution analysis of density operators, electron density, and energy functionals
Author(s) -
Nagy Szilvia,
Pipek János
Publication year - 2001
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.1406
Subject(s) - statistical physics , kinetic energy , wave function , wavelet , mathematics , physics , mathematical analysis , quantum mechanics , computer science , artificial intelligence
Abstract Numerical calculations show that, in extended electronic systems, complex one‐particle states appear with different shape characteristics at different length scales. New results in the theory of wavelets are applied in this contribution for a consistent description of densities and density operators with a continuous kernel at various length scales. It is proved here that, for real physical systems, according to physical intuition, neither arbitrarily fine nor arbitrarily rough details of the wave function and density operators can exist. It is also shown that the calculation of both kinetic energy and interaction energy expectation values can be reduced to the determination of some universal functions defined on integer‐valued arguments. © 2001 John Wiley & Sons, Inc. Int J Quant Chem, 2001