Communications in Mathematical Physics

, Volume 104, Issue 2, pp 283–290 | Cite as

Stability of coulomb systems with magnetic fields

III. Zero energy bound states of the Pauli operator
  • Michael Loss
  • Horng-Tzer Yau


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).


Magnetic Field Neural Network Statistical Physic Complex System Fine Structure 
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Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Michael Loss
    • 1
  • Horng-Tzer Yau
    • 1
  1. 1.Department of Mathematics and PhysicsPrinceton UniversityPrincetonUSA

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