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Semiclassical Mechanics with Molecular Applications 2nd Edition by Mark S Child ISBN 0199672989 9780199672981

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Semiclassical Mechanics with Molecular Applications 2nd Edition Mark S. Child Digital Instant Download

Author(s): Mark S. Child
ISBN(s): 9780199672981, 0199672989
Edition: 2
File Details: PDF, 11.25 MB
Year: 2014
Language: english
SKU: EB-5057076 Category: Tag:

Semiclassical Mechanics with Molecular Applications 2nd Edition by Mark S Child – Ebook PDF Instant Download/Delivery: 0199672989, 9780199672981
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ISBN 10: 0199672989 
ISBN 13: 9780199672981
Author: Mark S Child

The second edition of an established graduate text, this book complements the material for a typical advanced graduate course in quantum mechanics by showing how the underlying classical structure is reflected in quantum mechanical interference and tunnelling phenomena, and in the energy and angular momentum distributions of quantum mechanical states in the moderate to large (10-100) quantum number regime. Applications include accurate quantization techniques for a variety of tunnelling and curve-crossing problems and of non-separable bound systems; direct inversion of molecular scattering and spectroscopic data; wavepacket propagation techniques; and the prediction and interpretation of elastic, inelastic and chemically reactive scattering. The main text concentrates less on the mathematical foundations than on the global influence of the classical phase space structures on the quantum mechanical observables. Further mathematical detail is contained in the appendices and worked problem sets are included as an aid to the student.

Semiclassical Mechanics with Molecular Applications 2nd Table of 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
Isolated turning points
Potential well
Potential barrier
Behaviour at a potential singularity
2.4 Higher-order phase integral approximations
2.5 Problems
3 Quantization
3.1 Bohr–Sommerfeld quantization
Vibration
Rotation in a plane
Orbital motion
Steep-walled potentials
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 Problems
4 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 limits
6.4 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
Non-degenerate case
Degenerate case: the Birkoff–Gustavson normal form
7.6 Adiabatic switching
7.7 Periodic orbit quantization
Regular systems
Irregular systems
Periodic orbit scars
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 transitions
8.5 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
Primitive semiclassical approximation
Uniform Airy approximation
Glory scattering
Classically forbidden contributions
Complex angular momentum (Regge pole) theory
9.3 The integral cross-section
The background cross-section
Glory oscillations
Orbiting resonances
Exchange oscillations
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 identities
11.2 Nearside–farside interpretation of differential cross-sections
Arbitrary helicity indices
11.3 The influence of geometric phase on reactive scattering
11.4 Instanton theory of deep tunnelling
Eckart barrier
Miller theory
Kryvohuz modification
Connection with ring polymer theory
11.5 Problems

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