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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. doi:10.1007/s11005-011-0499-4.

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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
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URLURL TypeDescription Paper ReadCube access
Frank, Rupert L.0000-0001-7973-4688
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.
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
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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
Deposited On:01 May 2017 16:39
Last Modified:15 Nov 2021 17:28

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