Jump to ContentJump to Main Navigation
Semiclassical Mechanics with Molecular Applications$
Users without a subscription are not able to see the full content.

M. S. Child

Print publication date: 2014

Print ISBN-13: 9780199672981

Published to Oxford Scholarship Online: October 2014

DOI: 10.1093/acprof:oso/9780199672981.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2018. All Rights Reserved. Under the terms of the licence agreement, an individual user may print out a PDF of a single chapter of a monograph in OSO for personal use (for details see www.oxfordscholarship.com/page/privacy-policy).date: 14 November 2018

The classical S matrix

The classical S matrix

(p.242) 10 The classical S matrix
Semiclassical Mechanics with Molecular Applications

M. S. Child

Oxford University Press

The classical S matrix is a natural multidimensional extension of the semiclassical phase shift. It is most naturally interpreted as a contraction of the Feynman path integral propagator, between initial and final scattering states. An equivalent derivation in the text employs a multidimensional JWKB wavefunction in place of the propagator. The primitive semiclassical S matrix appears as a sum over classical trajectories, which interfere according to differences in their classical action integrals, while classically forbidden events are handled by the use of complex time trajectories. Appropriate uniform approximations to remove different types of singularity at the classical boundary are described. Symmetry selection rules are seen to arise from the physical equivalence of initial starting geometries. Applications to rotational rainbows and Condon reflection principles are given.

Keywords:   S matrix, Feynman path integral, JWKB, primitive semiclassical, uniform, caustic, complex time, rotational rainbow

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .