Number of Bound States of Schröedinger Operators with Matrix-Valued Potentials

Frank, Rupert L. and Lieb, Elliott H. and Seiringer, Robert (2007) Number of Bound States of Schröedinger Operators with Matrix-Valued Potentials. Letters in Mathematical Physics, 82 (2-3). pp. 107-116. ISSN 0377-9017. doi:10.1007/s11005-007-0211-x. https://resolver.caltech.edu/CaltechAUTHORS:20170510-095237526

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Abstract

We give a Cwikel–Lieb–Rozenblum type bound on the number of bound states of Schrödinger operators with matrix-valued potentials using the functional integral method of Lieb. This significantly improves the constant in this inequality obtained earlier by Hundertmark.

Item Type:

Article

Related URLs:

URL	URL Type	Description
https://doi.org/10.1007/s11005-007-0211-x	DOI	Article
https://rdcu.be/4zTe	Publisher	Free ReadCube access
https://arxiv.org/abs/0710.1877	arXiv	Discussion Paper

ORCID:

Author	ORCID
Frank, Rupert L.	0000-0001-7973-4688
Lieb, Elliott H.	0000-0001-5843-3587

Additional Information:

© 2007 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes. Received: 09 October 2007; Revised: 15 November 2007; Accepted: 16 November 2007. Dedicated to Jean-Claude Cortet, in appreciation of his contribution to Letters in Mathematical Physics. This work was supported by DAAD grant D/06/49117 (R.F.), by U.S. National Science Foundation grants PHY 06 52854 (E.L.) and PHY 06 52356 (R.S.), and by an A.P. Sloan Fellowship (R.S.).

Funders:

Funding Agency	Grant Number
Deutscher Akademischer Austauschdienst (DAAD)	D/06/49117
NSF	PHY-0652854
NSF	PHY-0652356
Alfred P. Sloan Foundation	UNSPECIFIED

Subject Keywords:

Schrödinger operator; Lieb–Thirring inequality; Cwikel–Lieb–Rozenblum inequality

Issue or Number:

2-3

Classification Code:

Mathematical Subject Classification (2000): Primary: 35P15. Secondary: 35J10; 47F05; 81Q10

DOI:

10.1007/s11005-007-0211-x

Record Number:

CaltechAUTHORS:20170510-095237526

Persistent URL:

https://resolver.caltech.edu/CaltechAUTHORS:20170510-095237526

Official Citation:

Frank, R.L., Lieb, E.H. & Seiringer, R. Lett Math Phys (2007) 82: 107. https://doi.org/10.1007/s11005-007-0211-x

Usage Policy:

No commercial reproduction, distribution, display or performance rights in this work are provided.

ID Code:

77336

Collection:

CaltechAUTHORS

Deposited By:

Ruth Sustaita

Deposited On:

12 May 2017 20:12

Last Modified:

15 Nov 2021 17:30

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