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April 2002 On the number of bound states for Schrödinger operators with operator-valued potentials
Dirk Hundertmark
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Ark. Mat. 40(1): 73-87 (April 2002). DOI: 10.1007/BF02384503

Abstract

Cwikel's bound is extended to an operator-valued setting. One application of this result is a semi-classical bound for the number of negative bound states for Schrödinger operators with operator-valued potentials. We recover Cwikel's bound for the Lieb-Thirring constant L0,3 which is far worse than the best available by Lieb (for scalar potentials). However, it leads to a uniform bound (in the dimension d≥3) for the quotient L0,d/Lcl0,d is the so-called classical constant. This gives some improvement in large dimensions.

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Dirk Hundertmark. "On the number of bound states for Schrödinger operators with operator-valued potentials." Ark. Mat. 40 (1) 73 - 87, April 2002. https://doi.org/10.1007/BF02384503

Information

Received: 6 November 2000; Published: April 2002
First available in Project Euclid: 31 January 2017

zbMATH: 1030.35129
MathSciNet: MR1948887
Digital Object Identifier: 10.1007/BF02384503

Rights: 2002 © Institut Mittag-Leffler

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Vol.40 • No. 1 • April 2002
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