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, 2019. 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: 20 February 2019

Matrix elements

Matrix elements

(p.99) 5 Matrix elements
Semiclassical Mechanics with Molecular Applications

M. S. Child

Oxford University Press

Two types of matrix element approximation are adopted according to whether the wavefunctions are taken in angle–action or normalized JWKB forms. The former gives the Heisenberg correspondence between matrix elements and classical Fourier components. The latter approximation is appropriate to situations for which the dominant contribution to the integral comes from stationary phase or ‘Condon’ points, at which both coordinates and momenta are conserved between the two states. The presence of a single such point leads to a ‘Condon reflection’ pattern such that the energy variation of the matrix element mimics the nodal pattern of the parent wavefunction. Complications arising from multiple Condon points are discussed.

Keywords:   Heisenberg correspondence, Fourier components, matrix elements, stationary phase, Condon point, Condon reflection

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 .