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On the use of multipole expansion of the Coulomb potential in quantum chemistry

โœ Scribed by Andrei V. Scherbinin; Vladimir I. Pupyshev; Nikolai F. Stepanov

Publisher
John Wiley and Sons
Year
1996
Tongue
English
Weight
777 KB
Volume
60
Category
Article
ISSN
0020-7608

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โœฆ Synopsis

Some features of the multipole expansion of the Coulomb potential V for a system of point charges are studied. It is shown that multipole expansion is convergent both locally in L,(R3) and weakly on some classes of functions. One-particle Hamiltonians H, = Ha + V,, where Ha is the kinetic energy operator and V, is the n-th partial sum of the multipole expansion of V , are discussed, and the convergence of their eigenvalues to those of H = H , + V with increasing n is proved. It is also shown that the discrete spectrum eigenfunctions of H, converge to those of H both in L,(R3) (together with their first and second derivatives) and uniformly on R3.

๐Ÿ“œ SIMILAR VOLUMES

Efficient evaluation of the acoustic rad
Efficient evaluation of the acoustic radiation using multipole expansion
โœ Michel A. Tournour; Noureddine Atalla ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 125 KB

The variational boundary element method (VBEM) is widely used to compute the acoustic radiation of structures. The classical numerical implementation of the VBEM su ers from the computational cost associated with double surface integration. In a previous paper [1], the authors proposed a novel metho