Jump to ContentJump to Main Navigation
Essential Quantum Mechanics$
Users without a subscription are not able to see the full content.

Gary Bowman

Print publication date: 2007

Print ISBN-13: 9780199228928

Published to Oxford Scholarship Online: January 2008

DOI: 10.1093/acprof:oso/9780199228928.001.0001

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: 16 July 2019

Commutators and Uncertainty Relations

Commutators and Uncertainty Relations

Chapter:
(p.82) 7 Commutators and Uncertainty Relations
Source:
Essential Quantum Mechanics
Author(s):

Gary E. Bowman

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199228928.003.0007

Commutators and uncertainty relations have sparked much debate and confusion as to their physical meaning. As such, this chapter focuses partly on historical and interpretational aspects. Because it is central to the uncertainty relations, the commutator — including its manifestation in matrix mechanics — is introduced first. It is emphasized that the commutator of two operators is generally another operator. The general form of the uncertainty relations is then introduced. These relations reflect the fact that probability distributions for different observables are generally not independent. Moreover, application of the uncertainty relations generally requires knowledge of the quantum state — a fact that is obscured by the well known position-momentum uncertainty relation. Various proposed physical interpretations of the uncertainty relations are then discussed. The chapter concludes with a brief reflection on the significance of the uncertainty relations.

Keywords:   matrix mechanics, observable, probability distribution, interpretation

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 .