Generalized Sturmians and atomic spectra - Avery, James (World Scientific, 2006)
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002
Includes bibliographical references (pages 213-231) and index
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 --