Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multiresolution analysis of electronic structure: semicardinal and
  wavelet bases   This article reviews recent developments in multiresolution analysis which
make it a powerful tool for the systematic treatment of the multiple
length-scales inherent in the electronic structure of matter. Although the
article focuses on electronic structure, the advances described are useful for
non-linear problems in the physical sciences in general. The new language and
notations introduced are well- suited for both formal manipulations and the
development of computer software using higher-level languages such as C++. The
discussion is self-contained, and all needed algorithms are specified
explicitly in terms of simple operators and illustrated with straightforward
diagrams which show the flow of data. Among the reviewed developments is the
construction of_exact_ multiresolution representations from extremely limited
samples of physical fields in real space. This new and profound result is the
critical advance in finally allowing systematic, all electron calculations to
compete in efficiency with state-of-the-art electronic structure calculations
which depend for their celerity upon freezing the core electronic degrees of
freedom. This review presents the theory of wavelets from a physical
perspective, provides a unified and self-contained treatment of non-linear
couplings and physical operators and introduces a modern framework for
effective single-particle theories of quantum mechanics.

2
The categories of this paper are: math
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin