Jump to ContentJump to Main Navigation
Time-Dependent Density-Functional TheoryConcepts and Applications$
Users without a subscription are not able to see the full content.

Carsten A. Ullrich

Print publication date: 2011

Print ISBN-13: 9780199563029

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780199563029.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2017. 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 http://www.oxfordscholarship.com/page/privacy-policy).date: 22 October 2017

Fundamental existence theorems

Fundamental existence theorems

(p.45) 3 Fundamental existence theorems
Time-Dependent Density-Functional Theory

Carsten A. Ullrich

Oxford University Press

This chapter deals with the fundamental existence theorems of time-dependent density-functional theory. The first section introduces some important quantum mechanical concepts of time-dependent many-body systems, such as the time-dependent Schrödinger equation, time evolution operators, the continuity equation, and local conservation laws. In the next section, the Runge-Gross theorem and the van Leeuwen theorem are proved. These theorems establish the one-to-one correspondence between time-dependent densities and time-dependent potentials, for given initial states. Therefore, the many-body Hamiltonian, and all quantities following from it, are formally expressible as functionals of the time-dependent density. The proofs of the Runge-Gross and the van Leeuwen theorems are discussed in detail, including some subtle points such as the question of v-representability and the Taylor expansion about the initial time.

Keywords:   time-dependent Schrödinger equation, time evolution, continuity equation, local conservation laws, Runge-Gross theorem, van Leeuwen theorem, one-to-one correspondence, time-dependent densities

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 .