Advertisement

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
Article

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).

Keywords

Magnetic Field Neural Network Statistical Physic Complex System Fine Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 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)Google Scholar
  2. 2.
    Lieb, E.: The number of bound states of one-body Schrödinger operators and the Weyl problem. Porc. Am. Math. Soc.36, 241–252 (1980)Google Scholar
  3. 3.
    Reed, M., Simon, B.: Methods of modern mathematical physics. Vol.IV. Analysis of operators. New York: Academic Press 1978Google Scholar
  4. 4.
    Vick, J.: Homology theory. New York: Academic Press 1973Google Scholar
  5. 5.
    Spivak, M.: A comprehensive introduction to differential geometry. Delaware: Publish or Perish, 1979Google Scholar
  6. 6.
    Gilbarg, D., Trudinger, N.: Elliptic partial differential equations of second order. Berlin, Heidelberg, New York: Springer 1977Google Scholar
  7. 7.
    Bethe, H., Salpeter, E.: Quantum mechanics of one- and two-electron atoms. New York: Plenum Press 1977Google Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

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

Personalised recommendations