Semiclassical Methods in Molecular Scattering and Spectroscopy

Inhaltsverzeichnis

Semiclassical and Higher Order Approximations: Properties. Solution of Connection Problems.- 1. Introduction.- 2. First order JWKB approximation.- 3. Method for solving connection problems.- 4. Anti-Stokes' and Stokes' Lines.- 5. Properties of the JWKB Approximation in the complex plane.- 6. Bohr-Sommerfeld quantization condition.- 7. Phase shift.- 8. Normalization.- 9. Expectation values and matrix elements.- 10. Higher order approximations.- 11. Exercises.- References.- Semiclassical Theory of Elastic Scattering.- 1. Introduction.- 2. Quantum mechanical elastic scattering.- 3. Classical elastic scattering.- 4. The semiclassical phase shift.- 5. Semiclassical evaluation of f(?).- 6. Orbiting collisions and resonances.- 7. Regge pole representation of f(?).- References.- Problems.- Applications of Bohr Quantization in Diatomic Molecule Spectroscopy.- 1. Introduction.- 2. Spectroscopic properties of the potential function.- 3. RKR inversion.- 4. Near dissociation behaviour of diatomic molecules.- 5. Problems.- References.- Separable Spectroscopy Applications.- 1. Frack-Condon factors and predissociation.- 2. Tunneling and curve-crossing problems.- 3. Problems.- References.- The Classical S Matrix.- 1. Classical considerations.- 2. Derivations of the S matrix.- 3. Problems.- References.- Semiclassical Theory of Eletronically Non-Adiabatic Transitions in Molecular Collisions Processes.- 1. Introductory concepts and tools.- 2. Specific theories and dynamical models.- 3. Miller-George theory of electronic transitions.- 4. Applications of the semiclassical S matrix.- 5. Interaction with fields. Laser-enhanced collisions.- 6. Miscellaneous aspects of laser-enhanced collisions.- Problems.- References.- Correspondence-Principle Methods for Molecular Collisions.- 1. Introduction.- 2. Bound states and matrix elements.- 3. Cross sections.- 4. Collinear vibrational excitation.- 5. Rotational excitation.- 6. Rotational-vibrational excitation and rotor-rotor collisions.- 7. Conclusions.- Problems.- References.- The Determination of Bound States by Semiclassical Methods.- 1. The nature of classical trajectories.- 2. Methods for determining semiclassical eigenvalues.- 3. Quantum effects of classical ergodicity.- References.- Appendix. M. S. Child/The Airy Function.- 1. Properties.- References.- Author Index.