Stability of coulomb systems with magnetic fields
- 96 Downloads
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 , collapse when the nuclear charge numberz≧9π2/8α2 (α is the fine structure constant).
KeywordsMagnetic Field Neural Network Statistical Physic Complex System Fine Structure
Unable to display preview. Download preview PDF.
- 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.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.Reed, M., Simon, B.: Methods of modern mathematical physics. Vol.IV. Analysis of operators. New York: Academic Press 1978Google Scholar
- 4.Vick, J.: Homology theory. New York: Academic Press 1973Google Scholar
- 5.Spivak, M.: A comprehensive introduction to differential geometry. Delaware: Publish or Perish, 1979Google Scholar
- 6.Gilbarg, D., Trudinger, N.: Elliptic partial differential equations of second order. Berlin, Heidelberg, New York: Springer 1977Google Scholar
- 7.Bethe, H., Salpeter, E.: Quantum mechanics of one- and two-electron atoms. New York: Plenum Press 1977Google Scholar