Hyperspherical Harmonics and Generalized Sturmians
Seiten
2002
Springer-Verlag New York Inc.
978-1-4020-0409-4 (ISBN)
Springer-Verlag New York Inc.
978-1-4020-0409-4 (ISBN)
Explores the connections between the theory of hyperspherical harmonics, momentum-space quantum theory, and generalized Sturmian basis functions. This work introduces methods, and the method of many-electron Sturmians offers an alternative to the usual SCF-CI methods for calculating atomic and molecular structure.
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 Lowdin [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-Lowdin 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.
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 Lowdin [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-Lowdin 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.
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.
| Reihe/Serie | Progress in Theoretical Chemistry and Physics ; 4 |
|---|---|
| Zusatzinfo | VIII, 196 p. |
| Verlagsort | New York, NY |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Naturwissenschaften ► Physik / Astronomie ► Astronomie / Astrophysik |
| Naturwissenschaften ► Physik / Astronomie ► Quantenphysik | |
| Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik | |
| ISBN-10 | 1-4020-0409-5 / 1402004095 |
| ISBN-13 | 978-1-4020-0409-4 / 9781402004094 |
| Zustand | Neuware |
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