Harmonic polynomials, hyperspherical harmonics, and atomic spectra

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:233

Article; Proceedings Paper

Avery, John Scales

关键词: Harmonic polynomials;    Hyperangular integration;    Hyperspherical harmonics;    Sturmians;    Atomic spectra;   

DOI  :  10.1016/j.cam.2009.02.057

来源: Elsevier

【 摘 要 】

The properties of monomials, homogeneous polynomials and harmonic polynomials in d-dimensional spaces are discussed. The properties are shown to lead to formulas for the canonical decomposition of homogeneous polynomials and formulas for harmonic projection. Many important properties of spherical harmonics, Gegenbauer polynomials and hyperspherical harmonics follow from these formulas. Harmonic projection also provides alternative ways of treating angular momentum and generalised angular momentum. Several powerful theorems for angular integration and hyperangular integration can be derived in this way. These purely mathematical considerations have important physical applications because hyperspherical harmonics are related to Coulomb Sturmians through the Fock projection, and because both Sturmians and generalised Sturmians have shown themselves to be extremely useful in the quantum theory of atoms and molecules. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

Free