Letters in Mathematical Physics

, Volume 11, Issue 4, pp 337–340 | Cite as

A remark on eigenvalue splittings for one-dimensional double-well Hamiltonians

  • Shu Nakamura
Article

Abstract

It is shown that the bound obtained by the WKB-method gives a correct lower bound on eigenvalue splittings for one-dimensional double-well Hamiltonians in the semiclassical limit. A modified version of the argument of Kirsch and Simon is employed.

Keywords

Statistical Physic Group Theory Semiclassical Limit Eigenvalue Splitting 

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References

  1. 1.
    KirschW. and SimonB.,Commun. Math. Phys. 97, 453–460 (1985).Google Scholar
  2. 2.
    HarrellE.,Commun. Math. Phys. 75, 239–261 (1980).Google Scholar
  3. 3.
    CombesJ. M., DuclosP., and SeilerR.,Commun. Math. Phys. 92, 229–245 (1983).Google Scholar
  4. 4.
    SimonB.,Ann. Math. 120, 89–118 (1984);J. Funct. Anal. 63, 123–136 (1985).Google Scholar
  5. 5.
    Protter, M. H. and Weinberger, H. F.,Maximum Principles in Differential Equations, Prentice-Hall, 1967.Google Scholar
  6. 6.
    HelfferB. and SjöstrandJ.,Commun. P.D.E. 9, 337–408 (1984).Google Scholar

Copyright information

© D. Reidel Publishing Company 1986

Authors and Affiliations

  • Shu Nakamura
    • 1
  1. 1.Department of Pure and Applied SciencesUniversity of TokyoTokyoJapan

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