Multiresolution analysis of density operators, electron density, and energy functionals

Numerical calculations show that, in extended electronic systems, complex o ne-particle states appear with different shape characteristics at different length scales. New results in the theory of wavelets are applied in this c ontribution 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 arbitr arily fine nor arbitrarily rough details of the wave function and density o perators can exist. It is also shown that the calculation of both kinetic e nergy and interaction energy expectation values can be reduced to the deter mination of some universal functions defined on integer-valued arguments. ( C) 2001 John Wiley & Sons, Inc.