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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.

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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
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URLURL TypeDescription ReadCube access Paper
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.).
Funding AgencyGrant Number
Deutscher Akademischer Austauschdienst (DAAD)D/06/49117
Alfred P. Sloan FoundationUNSPECIFIED
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
Record Number:CaltechAUTHORS:20170510-095237526
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Official Citation:Frank, R.L., Lieb, E.H. & Seiringer, R. Lett Math Phys (2007) 82: 107.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77336
Deposited By: Ruth Sustaita
Deposited On:12 May 2017 20:12
Last Modified:15 Nov 2021 17:30

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