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Symmetry of Intramolecular Quantum Dynamics.
The main goal of this book is to give a systematic description of intramolecular quantum dynamics on the basis of only the symmetry principles. In this respect, the book has no analogs in the world literature. The obtained models lead to a simple, purely algebraic, scheme of calculation and are rigo...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés Ruso |
| Publicado: |
Berlin :
De Gruyter,
2012.
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| Colección: | De Gruyter studies in mathematical physics.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Preface; I Foundations of the mathematical apparatus; 1 Basic concepts of group theory; 1.1 The group postulates; 1.2 Subgroup, direct product of groups, isomorphism, and homomorphism; 1.3 Cosets. Semidirect product of groups; 1.4 Conjugacy classes; 2 Basic concepts of group representation theory; 2.1 Linear vector spaces; 2.2 Operators in configuration and function spaces; 2.3 Representations of groups; 2.4 Characters. Decomposition of reducible representations; 2.5 Direct product of representations. Symmetric power; 2.6 The Clebsch-Gordan coefficients.
- 2.7 Basis functions of irreducible representations2.8 Irreducible tensor operators. The Wigner-Eckart theorem; 3 The permutation group; 3.1 Operations in the permutation group. Classes; 3.2 Irreducible representations. The Young diagrams and tableaux; 3.3 Basis functions of irreducible representations; 3.4 The conjugate representation; 4 Continuous groups; 4.1 Compact Lie groups; 4.2 Lie group of linear transformations; 4.3 Lie algebra. Three-dimensional rotation group; 4.4 Irreducible representations of a three-dimensional rotation group; 5 Point groups; 5.1 Operations in point groups.
- 5.2 Discrete axial groups5.3 Cubic groups. Icosahedral groups; 5.4 Continuous axial groups; 6 Dynamic groups; 6.1 Invariant dynamic groups; 6.2 Noninvariant dynamic groups; II Qualitative intramolecular quantum dynamics; 7 The philosophy of using the symmetry properties of internal dynamics; 7.1 Symmetry groups of internal dynamics; 7.2 Significance of the analysis of symmetry properties; 7.3 On the domain of the point group; 7.4 The chain of symmetry groups; 7.5 The concept of the coordinate spin; 7.6 The influence of numerical methods on the overall description; 7.7 Conclusions.
- 8 Internal dynamics of rigid molecules8.1 Nonlinear molecules without inversion center; 8.2 Nonlinear molecules with inversion center; 8.3 Linear molecules; 8.4 Description of quasidegenerate vibronic states; 8.5 Conclusions; 9 Molecules with torsional transitions of the exchange type; 9.1 Extended point groups. Intermediate configuration; 9.2 Methanol molecule CH3OH; 9.3 Ethane molecule C2H6; 9.4 The molecules of complex hydrides LiBH4 and NaBH4; 9.5 The molecules of dimethyl ether (CH3)2O and acetone (CH3)2CO; 9.6 Conclusions; 10 Molecules with pseudorotations of the exchange type.
- 10.1 Extended point groups10.2 Cyclobutane molecule C4H8; 10.3 Molecules of the XPF4 type; 10.4 Phosphorus pentafluoride molecule PF5; 10.5 The separation of internal motions; 10.6 Conclusions; 11 Molecules with transitions of the nonexchange type between equivalent configurations; 11.1 Extended point groups; 11.2 The ammonia molecule NH3; 11.3 The peroxide molecule HOOH; 11.4 The hydrazine molecule N2H4; 11.5 Conclusions; 12 On the meaning of the Born-Oppenheimer Approximation; 12.1 Nondegenerate electronic states; 12.2 Degenerate electronic states.