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Convexity Properties of Coulomb Systems

  • W. Thirring
Conference paper
Part of the Acta Physica Austriaca Supplementum XIV book series (FEWBODY, volume 14/1975)

Abstract

Usually when one calculates the eigenvalues Ej(α) of a Hamiltonian H = HO + αV, Ej(O) being known, one attempts a Taylor expansion: Ej(α) = Ej(O) + α Ej!(O)+... Unfortunately, even when this series converges, there is no garanty that the first few terms will be close to Ej(α). For instance, if Ej(α) is a rapidly oscillating function, a linear or parabolic approximation will evidently not be very good. However, for the ground state this cannot happen because of the

Keywords

Ground State Energy Concave Function Essential Spectrum Schrodinger Equation Convexity Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    W. Thirring, Acta Physica Austr. Suppl. XI, 493 (1973).Google Scholar
  2. 2.
    T.K. Rebane, Opt. Spec. (USSR) 34, 488 (1973).Google Scholar
  3. 3.
    A. Weinstein, W. Stenger, Intermediate Problems for Eigenvalues, Academic Press, New York (1972).MATHGoogle Scholar
  4. 4.
    W. Thirring, Vorlesungen über Mathematische Physik, T7.Google Scholar
  5. 5.
    H. Narnhofer, W. Thirring, Acta Physica Austr. 1975, Festschrift für P. Urban.Google Scholar

Copyright information

© Springer-Verlag 1975

Authors and Affiliations

  • W. Thirring
    • 1
  1. 1.Institut für Theoretische PhysikUniversität WienAustria

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