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Stability of Coulomb Systems with Magnetic Fields

I. The One-Electron Atom
  • Jürg Fröhlich
  • Elliott H. Lieb
  • Michael Loss

Abstract

The ground state energy of an atom in the presence of an external magnetic field B (with the electron spin-field interaction included) can be arbitrarily negative when B is arbitrarily large. We inquire whether stability can be restored by adding the self energy of the field, ∫ B 2. For a hydrogenic like atom we prove that there is a critical nuclear charge, z c , such that the atom is stable for z < z c , and unstable for z > z c .

Keywords

Magnetic Field Vector Field External Magnetic Field Ground State Energy Sobolev Inequality 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Jürg Fröhlich
    • 1
  • Elliott H. Lieb
    • 2
  • Michael Loss
    • 2
  1. 1.Theoretical PhysicsETH-HönggerbergZürichSwitzerland
  2. 2.Departments of Mathematics and PhysicsPrinceton UniversityPrincetonUSA

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