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Generalized Sturmians and atomic spectra /
This book describes the generalized Sturmian method, which offers a fresh approach to the calculation of atomic spectra. Generalized Sturmians are isoenergetic solutions to an approximate many-electron Schrodinger equation with a weighted potential. The weighting factors are chosen in such a way as...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Hackensack, NJ :
World Scientific,
©2006.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Preface
- 1. Historical background. 1.1. Sturm-Liouville theory. 1.2. The introduction of Sturmians into quantum theory. 1.3. One-electron Coulomb Sturmians. 1.4. Generalized Sturmians and many-particle problems. 1.5. Use of generalized Sturmian basis sets to solve the many-particle Schrödinger equation
- 2. Momentum space and iteration. 2.1. The d-dimensional Schrödinger equation in momentum space. 2.2. Momentum-space orthonormality relations for Sturmian basis sets. 2.3. Sturmian expansions of d-dimensional plane waves. 2.4. Iteration of the Schrödinger equation. 2.5. Generation of symmetry-adapted basis functions by iteration. 2.6. Solutions to the Sturmian secular equations obtained entirely by iteration
- 3. Generalized Sturmians applied to atomic spectra. 3.1. Goscinskian configurations with weighted nuclear charges. 3.2. Derivation of the secular equations. 3.3. Symmetry-adapted basis sets for the 2-electron isoelectronic series. 3.4. The large-Z approximation. 3.5. General symmetry-adapted basis sets derived from the large-Z approximation. 3.6. Symmetry-adapted basis functions from iteration
- 4. Autoionizing states. 4.1. Electron correlation and the molecule-like character of autoionizing states. 4.2. Calculation of autoionizing states using generalized Sturmians. 4.3. Higher series of [symbol]S autoionizing states
- 5. Core ionization. 5.1. Core ionization energies in the large-Z approximation. 5.2. Isonuclear series; piecewise-linear dependence of [symbol]E on N. 5.3. Core ionization energies for the 3-electron isoelectronic series
- 6. Strong external fields. 6.1. External electric fields. 6.2. Anomalous states. 6.3. Polarizabilities. 6.4. Induced transition dipole moments. 6.5. External magnetic fields
- 7. Relativistic effects. 7.1. Lorentz invariance and 4-vectors. 7.2. The Dirac equation for an electron in an external electromagnetic potential. 7.3. Time-independent problems. 7.4. The Dirac equation for an electron in the field of a nucleus. 7.5. Relativistic formulation of the Zeeman and Paschen-Bach effects. 7.6. Relativistic many-electron Sturmians. 7.7. A simple example. 7.8. Fine structure of spectral lines
- 8. Momentum space; the Fock transformation. 8.1. One-electron Coulomb Sturmians in direct space. 8.2. Fourier transforms of Coulomb Sturmians. 8.3. The Fock projection; hyperspherical harmonics. 8.4. The momentum-space orthonormality relations revisited
- 9. Harmonic polynomials. 9.1. Monomials, homogeneous polynomials, and harmonic polynomials. 9.2. The canonical decomposition of a homogeneous polynomial. 9.3. Generalized angular momentum. 9.4. Hyperangular integration
- 10. Hyperspherical harmonics. 10.1. The relationship between harmonic polynomials and hyperspherical harmonics. 10.2. Construction of hyperspherical harmonics by means of harmonic projection. 10.3. Hyperspherical harmonics in a 4-dimensional space. 10.4. Gegenbauer polynomials. 10.5. Hyperspherical expansion of a d-dimensional plane wave. 10.6. Alternative hyperspherical harmonics; the method of trees
- 11. The many-center problem. 11.1. The many-center one-electron problem. 11.2. Shibuya-Wulfrnan integrals. 11.3. Shibuya-Wulfrnan integrals and translations. 11.4. Matrix elements of the nuclear attraction potential. 11.5. The Sturmian secular equations for an electron moving in a many-center potential. 11.6. Molecular spectra.