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Communications in Mathematical Physics

, Volume 82, Issue 4, pp 457–469 | Cite as

Absence of discrete spectrum in highly negative ions

  • Mary Beth Ruskai
Article

Abstract

LetHN be the Hamiltonian for the Coulomb system consisting ofN particles of like charge in the field of a fixed point chargeZ. We show that if the particles are bosons, thenHN has no discrete spectrum whenNN0=cZ2 for some constantc. If the particles are fermions, thenHN is bounded below uniformly inN. These results can be extended to molecules and to other power law potentials.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing 
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.
    Uchiyama, J.: Publ. Res. Inst. Math. Sci. KyotoA5, 51–63 (1969)Google Scholar
  2. 2.
    Zhislin, G. M.: Teor. Mat. Fiz.7, 332–341 (1971); (Theor. Math. Phys.7, 571–578 (1971))Google Scholar
  3. 3.
    Yafaev, D. R.: Funkt. Anal. i Prilozeh.6, 103–104 (1972) (Funt. Anal. Appl.6, 349–350 (1972))Google Scholar
  4. 4.
    Hill, R. N.: Phys. Rev. Lett.38, 643–646 (1977); J. Math. Phys.18, 2316–2330 (1977)Google Scholar
  5. 5.
    Hill, R. N.: In: Mathematical Problems in Theoretical Physics, pp. 52–56. Berlin, Heidelberg, New York: Springer 1980.Google Scholar
  6. 6.
    Grosse, H., Pittner, L.: preprintGoogle Scholar
  7. 7.
    Hill, R. N.: private communication. See also [5]Google Scholar
  8. 8.
    Grosse, H.: J. Phys.A10, 711–716 (1977)Google Scholar
  9. 9.
    Yafaev, D.: Theor. Math. Phys. (USSR)27, 328–330 (1977)Google Scholar
  10. 10.
    Klaus, M., Simon, B.: Commun. Math. Phys.78, 153–168 (1980)Google Scholar
  11. 11.
    Hunziker, W.: Helv. Phys. Acta39, 451–462 (1966)Google Scholar
  12. 12.
    van Winter, C.: Mat.-Fys. Skr. Danske Vid. Selsk.1 (8), 1–60 (1964)Google Scholar
  13. 13.
    Zhislin, G.: Tr. Mosk. Mat. Obs.9, 81–128 (1960)Google Scholar
  14. 14.
    Reed, M., Simon, B.: Methods of modern mathematical physics IV. Analysis of operators. New York: Academic Press 1978Google Scholar
  15. 15.
    Uchiyama, J.: Publ. Res. Inst. Math. Sci. KyotoA6, 189–192 (1972)Google Scholar
  16. 16.
    Stillinger, F. H.: J. Chem. Phys.45, 3623–3631 (1966)Google Scholar
  17. 17.
    Ruskai, M. B.: (unpublished)Google Scholar
  18. 18.
    Vugal'ter, S. A., Zhislin, G. M.: Teor. Mat. Fiz.32, 70–87 (1977), (Theor. Math. Phys.32, 602–614 (1977))Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Mary Beth Ruskai
    • 1
  1. 1.The Rockefeller UniversityNew YorkUSA

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