Relativistic hydrogenic atoms in strong magnetic fields

Jean Dolbeault (1) , Maria J. Esteban (1) , Michael Loss (2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 School of Mathematics - Georgia Institute of Technology

In the Dirac operator framework we characterize and estimate the ground state energy of relativistic hydrogenic atoms in a constant magnetic field and describe the asymptotic regime corresponding to a large field strength using relativistic Landau levels. We also define and estimate a critical magnetic field beyond which stability is lost.

Mots clés: Dirac-Coulomb Hamiltonian; relativistic hydrogen atom; constant magnetic field; Landau levels; min-max levels; Hardy inequality; selfadjoint operators

Domaines: Equations aux dérivées partielles [math.AP]

Jean Dolbeault, Maria J. Esteban, Michael Loss. Relativistic hydrogenic atoms in strong magnetic fields. Annales Henri Poincaré, 2007, 8 (4), pp.749-779. ⟨hal-00083501⟩