On semi-classical bounds for eigenvalues of schrödinger operators

Michael Aizenman; Elliott H. Lieb

doi:10.1007/3-540-27056-6_17

On semi-classical bounds for eigenvalues of schrödinger operators

Michael Aizenman
, Elliott H. Lieb

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

Our principal result is that if the semiclassical estimate is a bound for some moment of the negative eigenvalues (as is known in some cases in one-dimension), then the semiclassical estimates are also bounds for all higher moments.

Original language	English (US)
Title of host publication	The Stability of Matter
Subtitle of host publication	From Atoms to Stars: Fourth Edition
Publisher	Springer Berlin Heidelberg
Pages	241-243
Number of pages	3
ISBN (Print)	3540420835, 9783540222125
DOIs	https://doi.org/10.1007/3-540-27056-6_17
State	Published - 2005

All Science Journal Classification (ASJC) codes

General Physics and Astronomy

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10.1007/3-540-27056-6_17

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title = "On semi-classical bounds for eigenvalues of schr{\"o}dinger operators",

abstract = "Our principal result is that if the semiclassical estimate is a bound for some moment of the negative eigenvalues (as is known in some cases in one-dimension), then the semiclassical estimates are also bounds for all higher moments.",

author = "Michael Aizenman and Lieb, \{Elliott H.\}",

note = "Funding Information: ¢' Work partly supported by U.S. National Science Foundation grant MCS 75-21684 A02.",

year = "2005",

doi = "10.1007/3-540-27056-6\_17",

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AU - Lieb, Elliott H.

N1 - Funding Information: ¢' Work partly supported by U.S. National Science Foundation grant MCS 75-21684 A02.

PY - 2005

Y1 - 2005

N2 - Our principal result is that if the semiclassical estimate is a bound for some moment of the negative eigenvalues (as is known in some cases in one-dimension), then the semiclassical estimates are also bounds for all higher moments.

AB - Our principal result is that if the semiclassical estimate is a bound for some moment of the negative eigenvalues (as is known in some cases in one-dimension), then the semiclassical estimates are also bounds for all higher moments.

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UR - https://www.scopus.com/pages/publications/84892195560#tab=citedBy

U2 - 10.1007/3-540-27056-6_17

DO - 10.1007/3-540-27056-6_17

M3 - Chapter

AN - SCOPUS:84892195560

SN - 3540420835

SN - 9783540222125

SP - 241

EP - 243

BT - The Stability of Matter

PB - Springer Berlin Heidelberg

ER -

On semi-classical bounds for eigenvalues of schrödinger operators

Abstract

All Science Journal Classification (ASJC) codes

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