Number of bound states of schrödinger operators with matrix-valued potentials

Rupert L. Frank; Elliott H. Lieb; Robert Seiringer

doi:10.1007/s11005-007-0211-x

Number of bound states of schrödinger operators with matrix-valued potentials

Rupert L. Frank, Elliott H. Lieb, Robert Seiringer

Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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.

Original language	English (US)
Pages (from-to)	107-116
Number of pages	10
Journal	Letters in Mathematical Physics
Volume	82
Issue number	2-3
DOIs	https://doi.org/10.1007/s11005-007-0211-x
State	Published - Dec 2007

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

Keywords

Cwikel-Lieb-Rozenblum inequality
Lieb-Thirring inequality
Schrödinger operator

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10.1007/s11005-007-0211-x

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@article{63de934c372b4421bd4af7518061afac,

title = "Number of bound states of schr{\"o}dinger operators with matrix-valued potentials",

abstract = "We give a Cwikel-Lieb-Rozenblum type bound on the number of bound states of Schr{\"o}dinger operators with matrix-valued potentials using the functional integral method of Lieb. This significantly improves the constant in this inequality obtained earlier by Hundertmark.",

keywords = "Cwikel-Lieb-Rozenblum inequality, Lieb-Thirring inequality, Schr{\"o}dinger operator",

author = "Frank, {Rupert L.} and Lieb, {Elliott H.} and Robert Seiringer",

note = "Funding Information: {\textcopyright}c 2007 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes. 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.).",

year = "2007",

month = dec,

doi = "10.1007/s11005-007-0211-x",

language = "English (US)",

volume = "82",

pages = "107--116",

journal = "Letters in Mathematical Physics",

issn = "0377-9017",

publisher = "Springer Netherlands",

number = "2-3",

}

TY - JOUR

T1 - Number of bound states of schrödinger operators with matrix-valued potentials

AU - Frank, Rupert L.

AU - Lieb, Elliott H.

AU - Seiringer, Robert

N1 - Funding Information: ©c 2007 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes. 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.).

PY - 2007/12

Y1 - 2007/12

N2 - 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.

AB - 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.

KW - Cwikel-Lieb-Rozenblum inequality

KW - Lieb-Thirring inequality

KW - Schrödinger operator

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U2 - 10.1007/s11005-007-0211-x

DO - 10.1007/s11005-007-0211-x

M3 - Article

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SN - 0377-9017

VL - 82

SP - 107

EP - 116

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

IS - 2-3

ER -

Number of bound states of schrödinger operators with matrix-valued potentials

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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