Semiclassical Mechanics with Molecular Applications (International Series of Monographs on Chemistry)

## Abstract 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 global influence of the classical phase space structures on the quantum mechanical observables. Further mathematical detail is contained in the appendices. Worked problem sets are included as an aid to the student. One important thread concerns the sharp separation between quantum interference in the classically accessible phase space and exponential decay into the inaccessible shadow regions. Another is the use of catastrophe theory to eliminate singularities at the classical boundaries between the two types of region. The theory goes on to show how different parts of the wavefunction may be stitched together to obtain accurate quantization formulae for a wide variety of tunnelling and curve-crossing problems. A careful account of classical angle–action transformations is extended to include the evaluation of matrix elements. A variety of extensions of the familiar spectroscopic RKR inversion procedure are given. It is also shown how bifurcations in the phase space structure signal changes in the quantum eigenvalue spectrum from, for example, normal mode to local mode behaviour. Other quantization techniques are shown to extend even to weakly chaotic systems. A chapter on Gaussian wavepacket propagation leads up to the currently popular Herman–Kluk technique. The book concludes with chapters on semiclassical aspects of elastic, inelastic and reactive scattering. 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. Title_Pages 2 Prefaces 6 Introduction 8 Phase integral approximations 15 Quantization 40 Angle–action variables 71 Matrix elements 106 Semiclassical inversion methods 130 Non-separable bound motion 149 Wavepackets 189 Atom–atom scattering 217 The classical S matrix 249 Reactive scattering 275 Phase integral techniques 306 Uniform approximations and diffraction integrals 329 Transformations in classical and quantum mechanics 351 The onset of chaos 381 Angle–action transformations 388 The monodromy matrix 393 Solutions to problems 396 References 417 Author index 429 Subject index 434 978–0–19–967298–1,-,Semiclassical,Mechanics,with,Molecular,Applications 978–0–19–967298–1 - Semiclassical Mechanics with Molecular Applications The second edition of a comprehensive text designed for advanced graduate courses in quantum mechanics. The title word 'semiclassical' highlights the novelty of the work which emphasizes the influence of classical mechanics on the behaviour of quantum mechanical systems.