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The Stability of Matter: From Atoms to Stars pp 241–243Cite as

On Semi-Classical Bounds for Eigenvalues of Schrödinger Operators

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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

  1. E.H. Lieb and W.E. Thirring, Phys. Rev. Lett. 35 (1975) 687. See Phys. Rev. Lett. 35 (1975) 1116 for errata. Also E.H. Lieb, Rev. Mod. Phys. 48 (1976) 553.

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  2. E.H. Lieb and W.E. Thirring, in: Studies in mathematical physics, Essays in honor of V. Bargmann (Princeton Univ. Press, Princeton, N.J., 1976).

    Google Scholar 

  3. A. Martin, Helv. Phys. Acta 45 (1972) 140.

    ADS  Google Scholar 

  4. H. Tamura, Proc. Japan Acad. 50 (1974) 19.

    Article  MATH  MathSciNet  Google Scholar 

  5. M. Cwikel, Ann. of Math. 106 (1977) 93.

    Article  MATH  MathSciNet  Google Scholar 

  6. E.H. Lieb, Bull. Amer. Math. Soc. 82 (1976) 751.

    Article  MATH  MathSciNet  Google Scholar 

  7. V. Glaser, H. Grosse and A. Martin, Bounds on the Number of Eigenvalues of the Schrödinger Operator, CERN preprint TH2432 (1977).

    Google Scholar 

  8. G.V. Rosenblum, The distribution of the discrete spectrum for singular differential operators, Isvestia Math. 164 No. 1 (1976) 75.

    Google Scholar 

  9. M.S. Birman and V.V. Borzov, On the asymptotics of the discrete spectrum of some singular differential operators, Topics in Math. Phys. 5 (1972) 19.

    MathSciNet  Google Scholar 

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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, 1090, Wien, Austria

    Walter Thirring

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© 2005 Springer-Verlag Berlin Heidelberg New York

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Aizenman, M., Lieb, E.H. (2005). 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/10.1007/3-540-27056-6_17

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  • DOI: https://doi.org/10.1007/3-540-27056-6_17

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22212-5

  • Online ISBN: 978-3-540-27056-0

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