UNSPECIFIED (1993) OPTIMIZED MULTICENTER EXPANSIONS. JOURNAL OF MATHEMATICAL PHYSICS, 34 (5). pp. 2004-2027. ISSN 0022-2488

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Abstract

A new approach to multicenter spherical harmonic expansions is presented, which is based on Fourier transform and variational methods. The individual radial functions are optimized simultaneously over all sites at each order of spherical harmonics; and it is conjectured that the resulting expansions, for arbitrary functions in three dimensions, will be more rapidly convergent than any other type. Both iterative and closed-form solutions are developed. The analogous cases for two- and one-dimensional functions are also treated and examples for all three cases are provided. The one-dimensional case is found to be qualitatively different. In a (perhaps) surprising theorem it is proved that, given N greater-than-or-equal-to 2 distinct points of R and N (not necessarily equivalent) choices of parity, an arbitrary one-dimensional function may be exactly decomposed as the sum of N functions each having one of the chosen parities at one of the points. The decomposition is not unique.

Item Type:	Journal Article
Subjects:	Q Science > QC Physics
Journal or Publication Title:	JOURNAL OF MATHEMATICAL PHYSICS
Publisher:	AMER INST PHYSICS
ISSN:	0022-2488
Date:	May 1993
Volume:	34
Number:	5
Number of Pages:	24
Page Range:	pp. 2004-2027
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/21375

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