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Stability of coulomb systems with magnetic fields

III. Zero energy bound states of the Pauli operator

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Abstract

It is shown that there exist magnetic fields of finite self energy for which the operator σ·(p−A) has a zero energy bound state. This has the consequence that single electron atoms, as treated recently by Fröhlich, Lieb, and Loss [1], collapse when the nuclear charge numberz≧9π2/8α2 (α is the fine structure constant).

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References

  1. Fröhlich, J., Lieb, E., Loss, M.: Stability of Coulomb systems with magnetic fields. I. The one-electron atom. Commun. Math. Phys.104, 251–270 (1986)

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Author notes

  1. Michael Loss

    Present address: Institut für Mathematik, FU Berlin, Arnimallee 3, D-100, Berlin 33

Authors and Affiliations

  1. Department of Mathematics and Physics, Princeton University, 08544, Princeton, NJ, USA

    Michael Loss & Horng-Tzer Yau

Authors
  1. Michael Loss
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  2. Horng-Tzer Yau
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Additional information

Communicated by A. Jaffe

Supported in part by the U.S. and Swiss NSF Cooperative Science Program No. INT-8503858.

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Loss, M., Yau, HT. Stability of coulomb systems with magnetic fields. Commun.Math. Phys. 104, 283–290 (1986). https://doi.org/10.1007/BF01211595

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  • DOI: https://doi.org/10.1007/BF01211595

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