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.
• 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(?).
• Problems.
• Applications of Bohr Quantization in Diatomic Molecule Spectroscopy.
• 2. Spectroscopic properties of the potential function.
• 3. RKR inversion.
• 4. Near dissociation behaviour of diatomic molecules.
• 5. Problems.
• Separable Spectroscopy Applications.
• 1. Frack-Condon factors and predissociation.
• 2. Tunneling and curve-crossing problems.
• 3. Problems.
• The Classical S Matrix.
• 1. Classical considerations.
• 2. Derivations of the S matrix.
• 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.
• Correspondence-Principle Methods for Molecular Collisions.
• 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.
• 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.
• Appendix. M. S. Child/The Airy Function.
• 1. Properties.
• Author Index.