Semiclassical mechanics with molecular applications

Semiclassical mechanics with molecular applications / Mark S. Child.

Semiclassical mechanics, which stems from the old quantum theory, has seen a remarkable revival in recent years as a physically intuitive and computationally accurate scheme for the interpretation of modern experiments. The main text concentrates less on the mathematical foundations than on the glob...

Full description

Saved in:
Bibliographic Details
Main Author: Child, M. S. (Author)
Format: eBook
Language:English
Published: Oxford : Oxford University Press, 2014.
Edition:Second edition.
Subjects:
Molecular spectroscopy.
Quantum chemistry.
SCIENCE > Chemistry > Physical & Theoretical.
Molecular spectroscopy
Quantum chemistry
Chemistry.
Physical Sciences & Mathematics.
Analytical Chemistry.
Online Access:Click for online access
Table of Contents:
  • Cover; Prefaces; Contents; 1 Introduction; 1.1 Classical and quantum mechanical structures; 1.2 Historical perspectives; 1.3 Scope and organization of the text; 2 Phase integral approximations; 2.1 The JWKB approximation; 2.2 Turning point behaviour; 2.3 Uniform approximations; 2.4 Higher-order phase integral approximations; 2.5 Problems; 3 Quantization; 3.1 Bohr-Sommerfeld quantization; 3.2 Semiclassical connection formulae; 3.3 Double minimum potentials and inversion doubling; 3.4 Restricted rotation; 3.5 Shape resonances or tunnelling predissociation; 3.6 Predissociation by curve crossing
  • 3.7 Problems4 Angle-action variables; 4.1 The linear oscillator; 4.2 The degenerate harmonic oscillator; 4.3 Angular momentum; 4.4 The hydrogen atom; 4.5 Symmetric and asymmetric tops; 4.6 Quantum monodromy; 4.7 Problems; 5 Matrix elements; 5.1 Semiclassical normalization; 5.2 Matrix elements and Fourier components: the Heisenberg correspondence; 5.3 Franck-Condon and curve-crossing matrix elements; 5.4 Matrix elements for non-curve-crossing situations; 5.5 Problems; 6 Semiclassical inversion methods; 6.1 The RKR method; 6.2 Inversion of predissociation linewidth and intensity data
  • 6.3 LeRoy-Bernstein extrapolation to dissociation limits6.4 Inversion of elastic scattering data; 6.5 Problems; 7 Non-separable bound motion; 7.1 Phase space structures; 7.2 Einstein-Brillouin-Keller quantization; 7.3 Uniform quantization at a resonance; 7.4 Fourier representation of the torus; 7.5 Classical perturbation theory; 7.6 Adiabatic switching; 7.7 Periodic orbit quantization; 7.8 Problems; 8 Wavepackets; 8.1 The free-motion Gaussian wavepacket; 8.2 Gaussian wavepackets and coherent harmonic oscillator states; 8.3 Seeded Gaussian wavefunctions and spectral quantization
  • 8.4 Franck-Condon transitions8.5 The Herman-Kluk propagator; 8.6 Problems; 9 Atom-atom scattering; 9.1 The classical and quantum mechanical limits; 9.2 Rainbow scattering and diffraction oscillations; 9.3 The integral cross-section; 9.4 Two-state non-adiabatic transitions; 9.5 Problems; 10 The classical S matrix; 10.1 The integral representation; 10.2 Stationary phase and uniform approximations; 10.3 Classically forbidden events; 10.4 Rotational rainbows and higher interference structures; 10.5 Condon reflection principles; 10.6 Problems; 11 Reactive scattering
  • 11.1 Definitions and working identities11.2 Nearside-farside interpretation of differential cross-sections; 11.3 The influence of geometric phase on reactive scattering; 11.4 Instanton theory of deep tunnelling; 11.5 Problems; Appendix A Phase integral techniques; A.1 The Stokes phenomenon; A.2 Isolated turning points; A.3 Barrier penetration; A.4 The linear oscillator; A.5 Curve crossing; Appendix B Uniform approximations and diffraction integrals; B.1 The uniform Airy approximation; B.2 Waves and catastrophes; B.3 Higher catastrophe-based uniform approximations

Similar Items