Hyperspherical harmonics and generalized Sturmians

by John Avery

"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 st