Communications in Mathematical Physics

, Volume 79, Issue 4, pp 529–572 | Cite as

Schrödinger operators with magnetic fields

III. Atoms in homogeneous magnetic field
  • J. E. Avron
  • I. W. Herbst
  • B. Simon


We prove a large number of results about atoms in constant magnetic field including (i) Asymptotic formula for the ground state energy of Hydrogen in large field, (ii) Proof that the ground state of Hydrogen in an arbitrary constant field hasL z = 0 and of the monotonicity of the binding energy as a function ofB, (iii) Borel summability of Zeeman series in arbitrary atoms, (iv) Dilation analyticity for arbitrary atoms with infinite nuclear mass, and (v) Proof that every once negatively charged ion has infinitely many bound states in non-zero magnetic field with estimates of the binding energy for smallB and largeL z .


Hydrogen Magnetic Field Neural Network Binding Energy Complex System 
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Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • J. E. Avron
    • 1
  • I. W. Herbst
    • 2
  • B. Simon
    • 3
  1. 1.Department of PhysicsPrinceton UniversityPrincetonUSA
  2. 2.Department of MathematicsUniversity of ViginiaCharlottesvilleUSA
  3. 3.Department of Mathematics and PhysicsPrinceton UniversityPrincetonUSA

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