Hyperspherical Harmonics and Generalized Sturmians / Edition 1

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Overview

This book explores the connections between the theory of hyperspherical harmonics, momentum-space quantum theory, and generalized Sturmian basis functions; and it introduces methods which may be used to solve many-particle problems directly, without the use of the self-consistent-field approximation. The method of many-electron Sturmians offers an interesting and fresh alternative to the usual SCF-CI methods for calculating atomic and molecular structure. When many-electron Sturmians are used, and when the basis potential is chosen to be the attractive potential of the nuclei in the system, the following advantages are offered: the matrix representation of the nuclear attraction potential is diagonal; the kinetic energy term vanishes from the secular equation; the Slater exponents of the atomic orbitals are automatically optimized; convergence is rapid; a correlated solution to the many-electron problem can be obtained directly, without the use of the SCF approximation; and excited states can be obtained with good accuracy.

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Editorial Reviews

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"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)
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Product Details

Table of Contents

Introduction. 1. Many-Particle Sturmians. 2. Momentum-Space Wave Functions. 3. Hyperspherical Harmonics. 4. The Momentum-Space Wave Equation. 5. Many-Center Potentials. 6. Iteration of the Wave Equation. 7. Molecular Sturmians. 8. Relativistic Effects. A. Generalized Slater-Condon Rules. B. Coulomb and Exchange Integrals for Atoms. Solutions to the Exercises. Bibliography. Index.

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