Hyperspherical Harmonics and Generalized Sturmians

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.

From the reviews:
"This book should find its place on the shelves of theoretical chemists as a good companion to other well-known books by this author: "Creation and annihilation operators" and "Quantum theory of atoms, molecules and photons"."
(Theoretical Chemistry Accounts, 106:236 (2001)

Résumé
Explores the connections between the theory of hyperspherical harmonics, momentum-space quantum theory, and generalized Sturmian basis functions. This book introduces methods which may be used to solve many-particle problems directly, without the use of the self-consistent-field approximation.

Contenu
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.