Hyperspherical Harmonics and Generalized Sturmians

2002
ISBN: 978-1-4020-0409-4
Verlag: Springer Netherlands

Buch, Englisch, Band 4, 196 Seiten, Paperback, Format (B × H): 155 mm x 233 mm, Gewicht: 321 g

Reihe: Progress in Theoretical Chemistry and Physics

n Angular Momentum Theory for Diatomic Molecules, R R method of trees, 3 construct the wave functions of more complicated systems for ex- ple many electron atoms or molecules. However, it was soon realized that unless the continuum is included, a set of hydrogenlike orbitals is not complete. To remedy this defect, Shull and Löwdin [273] - troduced sets of radial functions which could be expressed in terms of Laguerre polynomials multiplied by exponential factors. The sets were constructed in such a way as to be complete, i. e. any radial fu- tion obeying the appropriate boundary conditions could be expanded in terms of the Shull-Löwdin basis sets. Later Rotenberg [256, 257] gave the name “Sturmian” to basis sets of this type in order to emp- size their connection with Sturm-Liouville theory. There is a large and rapidly-growing literature on Sturmian basis functions; and selections from this literature are cited in the bibliography. In 1968, Goscinski [138] completed a study ofthe properties ofSt- rnian basis sets, formulating the problem in such a way as to make generalization of the concept very easy. In the present text, we shall follow Goscinski’s easily generalizable definition of Sturmians.

Zielgruppe

Research

Autoren/Hrsg.

Avery, John S.

Fachgebiete

• Naturwissenschaften Chemie Physikalische Chemie
• Naturwissenschaften Physik Thermodynamik Plasmaphysik
• Mathematik | Informatik Mathematik Mathematische Analysis Moderne Anwendungen der Analysis
• Naturwissenschaften Physik Quantenphysik Atom- und Molekülphysik
• Naturwissenschaften Physik Quantenphysik Kernphysik

Inhaltsverzeichnis

Many-particle Sturmians.- Momentum-space Wave Functions.- Hyperspherical Harmonics.- The Momentum-space Wave Equation.- Many-center Potentials.- Iteration of the Wave Equation.- Molecular Sturmians.- Relativistic Effects.