| Description |
1 online resource (xvi, 240 pages) : illustrations |
| Contents |
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 |
| Summary |
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 to make all of the solutions correspond to a given energy. The advantage of such an isoenergetic basis set is that every basis function has the correct turning point behavior needed for efficient synthesis of the wave function. The book also discusses methods for automatic generation of symmetry-adapted basis sets. Calculations using the generalized Sturmian method are presented and compared with experimental results from the NIST database. The relationship of Sturmians to harmonic polynomials and hyperspherical harmonics is also described. Methods for treating angular functions and angular integrals by means of harmonic projection are discussed, and these methods are shown to be especially useful for relativistic calculations. A final chapter discusses application of the generalized Sturmian method to the calculation of molecular spectra |
| Bibliography |
Includes bibliographical references (pages 213-231) and index |
| Notes |
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. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL |
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English |
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digitized 2010 HathiTrust Digital Library committed to preserve pda MiAaHDL |
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Print version record |
| Subject |
Quantum theory -- Mathematics
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Schrödinger equation.
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Atomic spectra.
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SCIENCE -- Physics -- Quantum Theory.
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Atomic spectra
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Quantum theory -- Mathematics
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Schrödinger equation
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Atomspektrum
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Sturm-Liouville-Problem
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| Form |
Electronic book
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| Author |
Avery, John, 1933-
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| LC no. |
2006048636 |
| ISBN |
9789812773593 |
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9812773592 |
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1281378917 |
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9781281378910 |
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9786611378912 |
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661137891X |
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