| Introduction / 1： |
| Classical and quantum mechanical structures / 1.1： |
| Historical perspectives / 1.2： |
| Scope and organization of the text / 1.3： |
| Phase integral approximations / 2： |
| The JWKB approximation / 2.1： |
| Turning point behaviour / 2.2： |
| Uniform approximations / 2.3： |
| Higher-order phase integral approximations / 2.4： |
| Problems / 2.5： |
| Quantization / 3： |
| Bohr-Sommerfeld quantization / 3.1： |
| Semiclassical connection formulae / 3.2： |
| Double minimum potentials and inversion doubling / 3.3： |
| Restricted rotation / 3.4： |
| Shape resonances or tunnelling predissociation / 3.5： |
| Predissociation by curve crossing / 3.6： |
| Angle-action variables / 3.7： |
| The linear oscillator / 4.1： |
| The degenerate harmonic oscillator / 4.2： |
| Angular momentum / 4.3： |
| The hydrogen atom / 4.4： |
| Symmetric and asymmetric tops / 4.5： |
| Quantum monodromy / 4.6： |
| Matrix elements / 4.7： |
| Semiclassical normalization / 5.1： |
| Matrix elements and Fourier components: the Heisenberg correspondence / 5.2： |
| Franck-Condori and curve-crossing matrix elements / 5.3： |
| Matrix elements for non-curve-crossing situations / 5.4： |
| Semiclassical inversion methods / 5.5： |
| The RKR method / 6.1： |
| Inversion of predissociation linewidth and intensity data / 6.2： |
| LeRoy-Bernstein extrapolation to dissociation limits / 6.3： |
| Inversion of elastic scattering data / 6.4： |
| Non-separable bound motion / 6.5： |
| Phase space structures / 7.1： |
| Einstein-Brillouin-Keller quantization / 7.2： |
| Uniform quantization at a resonance / 7.3： |
| Fourier representation of the torus / 7.4： |
| Classical perturbation theory / 7.5： |
| Adiabatic switching / 7.6： |
| Periodic orbit quantization / 7.7： |
| Wavepackets / 7.8： |
| The free-motion Gaussian wavepacket / 8.1： |
| Gaussian wavepackets and coherent harmonic oscillator states / 8.2： |
| Seeded Gaussian wavefunctions and spectral quantization / 8.3： |
| Franck-Condon transitions / 8.4： |
| The Herman- Kluk propagator / 8.5： |
| Atom-atom scattering / 8.6： |
| The classical and quantum mechanical limits / 9.1： |
| Rainbow scattering and diffraction oscillations / 9.2： |
| The integral cross-section / 9.3： |
| Two-state non-adiabatic transitions / 9.4： |
| The classical S matrix / 9.5： |
| The integral representation / 10.4： |
| Stationary phase and uniform approximations / 10.2： |
| Classically forbidden events / 10.3： |
| Rotational rainbows and higher interference structures / 40.2： |
| Condon reflection principles |
| Reactive scattering / 10.6： |
| Definitions and working identities / 11.1： |
| Nearside-farside interpretation of differential cross-sections / 11.2： |
| The influence of geometric phase on reactive scattering / 11.3： |
| Instanton theory of deep tunnelling / 11.4： |
| Phase integral techniques / 11.5： |
| The Stokes phenomenon / A.1： |
| Isolated turning points / A.2： |
| Barrier penetration / A.3： |
| Curve crossing / A.4： |
| Uniform approximations and diffraction integrals / Appendix B： |
| The uniform Airy approximation / B.4： |
| Waves and catastrophes / B.2： |
| Higher catastrophe-based uniform approximations / B.3： |
| Non-generic uniform approximations: Bessel and harmonic approximations |
| Transformations in classical and quantum mechanics / Appendix C： |
| Classical and semiclassical transformations / C.1： |
| Energy-time and angle-action representations / C.2： |
| Dynamical transformations and the classical S matrix / C.3： |
| The semiclassical Green's function / C.4： |
| Angular momentum coupling coefficients / C.5： |
| The onset of chaos / Appendix D： |
| Breaking the separatrix / D.4： |
| Henon map and the separatrix algorithm / D.2： |
| Angle-action transformations / Appendix E： |
| Harmonic oscillator / E.1： |
| Morse oscillator / E.2： |
| Degenerate harmonic oscillator / E.3： |
| Hydrogen atom / E.4： |
| The monodromy matrix / Appendix F： |
| Solutions to problems / Appendix G： |
| Atom- atom scattering / G.1： |
| References / G.10： |
| Author index |
| Subject index |
| Introduction / 1： |
| Classical and quantum mechanical structures / 1.1： |
| Historical perspectives / 1.2： |
