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On Semi-Classical Bounds for Eigenvalues of Schrödinger Operators

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The Stability of Matter: From Atoms to Stars

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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.

Work partly supported by U.S. National Science Foundation grant MCS 75-21684 A02.

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References

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Author information

Authors and Affiliations

  1. Department of Physics, Princeton University, Princeton, NJ, 08540, USA

    Michael Aizenman

  2. Departments of Mathematics and Physics, Princeton University, Princeton, NJ, 08540, USA

    Elliott H. Lieb

Authors
  1. Michael Aizenman
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  2. Elliott H. Lieb
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Editor information

Editors and Affiliations

  1. Institut für Theoretische Physik, Universität Wien, Boltzmanngasse 5, A-1090, Wien, Austria

    Walter Thirring

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© 1997 Springer-Verlag Berlin Heidelberg

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Aizenman, M., Lieb, E.H. (1997). On Semi-Classical Bounds for Eigenvalues of Schrödinger Operators. In: Thirring, W. (eds) The Stability of Matter: From Atoms to Stars. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03436-1_18

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  • DOI: https://doi.org/10.1007/978-3-662-03436-1_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-03438-5

  • Online ISBN: 978-3-662-03436-1

  • eBook Packages: Springer Book Archive

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