| Hyperspherical Harmonics and Generalized Sturmians 2002 Edition Contributor(s): Avery, John S. (Author) |
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ISBN: 1402004095 ISBN-13: 9781402004094 Publisher: Springer OUR PRICE: $52.24 Product Type: Paperback - Other Formats Published: May 2002 Annotation: 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. |
| Additional Information |
| BISAC Categories: - Science | Chemistry - Physical & Theoretical - Science | Physics - Quantum Theory - Mathematics | Mathematical Analysis |
| Dewey: 541.28 |
| Series: Progress in Theoretical Chemistry and Physics |
| Physical Information: 0.51" H x 6.14" W x 9.22" (0.65 lbs) 196 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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 L wdin 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-L wdin 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. |