J ul 1 99 8 Multiresolution analysis of electronic structure : semicardinal and wavelet bases

This article reviews the recent development of multiresolution analysis into an efficient and powerful tool for the systematic treatment of the multiple length-scales inherent in the electronic structure of matter. The article presents the mathematical theory of wavelets in a new language, suited to problems in the physical sciences and developed specifically for this review , and describes in full detail procedures for applying physical operators in multiresolution bases. In addition, a new basis-set independent notation for effective single-particle theories of quantum mechanics is developed in the course of the review. The discussion herein aims to be self-contained and to stimulate the use of multiresolution analysis in the study of electronic structure and other continuum problems in the physical sciences.