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Absence of discrete spectrum in highly negative ions

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Abstract

LetH N 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, thenH N has no discrete spectrum whenN≧N 0=cZ 2 for some constantc. If the particles are fermions, thenH N is bounded below uniformly inN. These results can be extended to molecules and to other power law potentials.

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Authors and Affiliations

  1. The Rockefeller University, 10021, New York, NY, USA

    Mary Beth Ruskai

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  1. Mary Beth Ruskai
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Communicated by E. Lieb

Research supported by the National Science Foundation, MCS78 -20455 USA

On leave from Department of Mathematics, University of Lowell, Lowell, MA O1854 USA

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Ruskai, M.B. Absence of discrete spectrum in highly negative ions. Commun.Math. Phys. 82, 457–469 (1982). https://doi.org/10.1007/BF01961235

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  • DOI: https://doi.org/10.1007/BF01961235

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