Hyperspherical harmonics and generalized sturmians
著者
書誌事項
Hyperspherical harmonics and generalized sturmians
（Progress in theoretical chemistry and physics, v. 4）
Kluwer Academic Publishers, c2000
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注記
Includes bibliographical references ( p. [163]-192) and index
内容説明・目次
内容説明
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.
目次
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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