On semi-classical bounds for eigenvalues of Schrödinger operators

Michael Aizenman; Elliott H. Lieb

doi:10.1016/0375-9601(78)90385-7

On semi-classical bounds for eigenvalues of Schrödinger operators

Michael Aizenman, Elliott H. Lieb

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

78 Scopus citations

Abstract

Our principal results 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)
Pages (from-to)	427-429
Number of pages	3
Journal	Physics Letters A
Volume	66
Issue number	6
DOIs	https://doi.org/10.1016/0375-9601(78)90385-7
State	Published - Jun 26 1978

All Science Journal Classification (ASJC) codes

Physics and Astronomy(all)

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10.1016/0375-9601(78)90385-7

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

abstract = "Our principal results 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 = "1978",

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doi = "10.1016/0375-9601(78)90385-7",

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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 - 1978/6/26

Y1 - 1978/6/26

N2 - Our principal results 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 results 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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U2 - 10.1016/0375-9601(78)90385-7

DO - 10.1016/0375-9601(78)90385-7

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SN - 0375-9601

VL - 66

SP - 427

EP - 429

JO - Physics Letters A

JF - Physics Letters A

IS - 6

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On semi-classical bounds for eigenvalues of Schrödinger operators

Abstract

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