On semi-classical bounds for eigenvalues of schrödinger operators

Michael Aizenman, Elliott Lieb

Research output: Chapter in Book/Report/Conference proceedingChapter

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 languageEnglish (US)
Title of host publicationThe Stability of Matter
Subtitle of host publicationFrom Atoms to Stars: Fourth Edition
PublisherSpringer Berlin Heidelberg
Pages241-243
Number of pages3
ISBN (Print)3540420835, 9783540222125
DOIs
StatePublished - Jan 1 2005

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Moment
Eigenvalue
Operator
Estimate
One Dimension

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Cite this

Aizenman, M., & Lieb, E. (2005). On semi-classical bounds for eigenvalues of schrödinger operators. In The Stability of Matter: From Atoms to Stars: Fourth Edition (pp. 241-243). Springer Berlin Heidelberg. https://doi.org/10.1007/3-540-27056-6_17
Aizenman, Michael ; Lieb, Elliott. / On semi-classical bounds for eigenvalues of schrödinger operators. The Stability of Matter: From Atoms to Stars: Fourth Edition. Springer Berlin Heidelberg, 2005. pp. 241-243
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Aizenman, M & Lieb, E 2005, On semi-classical bounds for eigenvalues of schrödinger operators. in The Stability of Matter: From Atoms to Stars: Fourth Edition. Springer Berlin Heidelberg, pp. 241-243. https://doi.org/10.1007/3-540-27056-6_17

On semi-classical bounds for eigenvalues of schrödinger operators. / Aizenman, Michael; Lieb, Elliott.

The Stability of Matter: From Atoms to Stars: Fourth Edition. Springer Berlin Heidelberg, 2005. p. 241-243.

Research output: Chapter in Book/Report/Conference proceedingChapter

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Aizenman M, Lieb E. On semi-classical bounds for eigenvalues of schrödinger operators. In The Stability of Matter: From Atoms to Stars: Fourth Edition. Springer Berlin Heidelberg. 2005. p. 241-243 https://doi.org/10.1007/3-540-27056-6_17