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Some new bounds on the number of bound states

  • K. Chadan
  • R. Kobayashi
Chapter
Part of the Springer Tracts in Modern Physics book series (STMP, volume 119)

Abstract

In this work, we generalize the well-known bounds of Glaser, Grosse, Martin, and Thirring on the number of bound states of a particle in a spherically symmetric potential. The new bounds fill the gap between the above bounds, and the Calogero bound.

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References

  1. [1]
    Glaser, V., Grosse, H., Martin, A., Thirring, W.: in “Essays in Honor of Valentine Bargmann” /1976/, edited by E.H. Lieb, B. Simon, and A.S. Wightman (Princeton University Press, Princeton).Google Scholar
  2. [2]
    Calogero, F. /1965/: Comm. Math. Phys. 1, 80.MATHCrossRefADSMathSciNetGoogle Scholar
  3. [3]
    Calogero, F. /1967/: The Variable Phase Approach to Potential Scattering (Academic Press, New York).Google Scholar
  4. [4]
    Chadan, K. /1968/: Nuovo Cimento, 58A, 191.ADSGoogle Scholar
  5. [5]
    Frank, W. M. /1967/: J. Math. Phys. 8, 466.MATHCrossRefADSGoogle Scholar
  6. [6]
    Martin, A. /1972/: Helv. Phys. Acta 45, 142.Google Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • K. Chadan
    • 1
  • R. Kobayashi
    • 2
  1. 1.Laboratoire de Physique Théorique et Hautes EnergiesUniversité de Paris XIOrsay CedexFrance
  2. 2.Department of MathematicsScience University of TokyoNoda, ChibaJapan

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