Jump to ContentJump to Main Navigation
Introduction to Scanning Tunneling MicroscopySecond Edition$
Users without a subscription are not able to see the full content.

C. Julian Chen

Print publication date: 2007

Print ISBN-13: 9780199211500

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780199211500.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2019. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 19 November 2019

Tunneling Matrix Elements

Tunneling Matrix Elements

Chapter:
(p.77) Chapter 3 Tunneling Matrix Elements
Source:
Introduction to Scanning Tunneling Microscopy
Author(s):

C. Julian Chen

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199211500.003.0003

This chapter presents systematic methods to evaluate the tunneling matrix elements in the Bardeen tunneling theory. A key problem in applying the Bardeen tunneling theory to STM is the evaluation of the tunneling matrix elements, which is a surface integral of the wavefunctions of the tip and the sample, roughly in the middle of the tunneling gap. By expanding the tip wavefunction in terms of spherical harmonics and spherical modified Bessel functions, very simple analytic expressions for the tunneling matrix elements are derived: the tunneling matrix elements are proportional to the amplitudes or the corresponding x-, y-, or z-derivatives of the sample wavefunction at the center of the tip. Two proofs are presented. The first proof is based on the Green's function of the Schrödinger's equation in vacuum. The second proof is based on a power-series expansion of the tip wavefunctions.

Keywords:   derivative rule, spherical harmonics, spherical modified Bessel functions, Green's function, tip wavefunctions, sample wavefunctions, sum rule

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 .