Adiabatic spectrum for relativistic hydrogen in a strong homogeneous magnetic field

Abstract

We study the bound states of relativistic hydrogen-like atoms coupled to strong homogeneous magnetic fields, assuming a fixed, infinitely heavy nucleus. Working in the adiabatic approximation in which the electron is confined to the lowest Landau level, we show that the corresponding Dirac Hamiltonian always has an infinite discrete spectrum accumulating at mc 2, m being the electron mass, and that, as the field strength increases, its eigenvalues successively descend into the lower part of the continuous spectrum, (−∞, −mc 2]. This phenomenon is for large B roughly periodical in log B.