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Eigenvalue bounds for Schrödinger operators with a homogeneous magnetic field

Frank, Rupert L. and Olofsson, Rikard (2011) Eigenvalue bounds for Schrödinger operators with a homogeneous magnetic field. Letters in Mathematical Physics, 97 . pp. 227-241. ISSN 0377-9017 . https://resolver.caltech.edu/CaltechAUTHORS:20170501-072120225

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Abstract

We prove Lieb-Thirring inequalities for Schrödinger operators with a homogeneous magnetic field in two and three space dimensions. The inequalities bound sums of eigenvalues by a semi-classical approximation which depends on the strength of the magnetic field, and hence quantifies the diamagnetic behavior of the system. For a harmonic oscillator in a homogenous magnetic field, we obtain the sharp constants in the inequalities.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1007/s11005-011-0499-4DOIArticle
http://link.springer.com/article/10.1007%2Fs11005-011-0499-4PublisherArticle
https://arxiv.org/abs/1102.0329arXivDiscussion Paper
http://rdcu.be/rIuaPublisherFree ReadCube access
Additional Information:© 2011 The Author(s). This paper may be reproduced, in its entirety, for non-commercial purposes. Received: 13 January 2011; Revised: 10 May 2011; Accepted: 10 May 2011. Published online: 9 June 2011. R. Olofsson acknowledges support through the Swedish Research Council.
Funders:
Funding AgencyGrant Number
Swedish Research CouncilUNSPECIFIED
Subject Keywords:Schrödinger operator; Lieb-Thirring inequalities; magnetic field
Classification Code:Mathematics Subject Classification (2000): Primary 35P15; Secondary 35J10; 81Q10
Record Number:CaltechAUTHORS:20170501-072120225
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170501-072120225
Official Citation:Frank, R.L. & Olofsson, R. Lett Math Phys (2011) 97: 227. doi:10.1007/s11005-011-0499-4
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77082
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:01 May 2017 16:39
Last Modified:03 Oct 2019 17:53

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