Stability of Coulomb Systems with Magnetic Fields
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 .
KeywordsMagnetic Field Vector Field External Magnetic Field Ground State Energy Sobolev Inequality
Unable to display preview. Download preview PDF.
- 4.Kato, T.: Schrödinger operators with singular potentials. Israel J. Math. 13, 135–148 (1972)Google Scholar
- 7.Lieb, E.H., Thirring, W.: Inequalities for the moments of the eigenvalues of the Schrödinger Hamiltonian and their relation to Sobolev inequalities. In: Studies in mathematical physics, essays in honor of Valentine Bargmann. Lieb, E.H., Simon, B., Wightman, A.S. (eds.). Princeton, NJ: Princeton University Press 1976Google Scholar
- 10.Stein, E.M.: Singular integrals and differentiability properties of functions. Princeton, NJ: Princeton University Press 1970Google Scholar