On the Ordering of Energy Levels in Homogeneous Magnetic Elds

We study the energy levels of a single particle in a homogeneous magnetic eld and in an axially symmetric external potential. For potentials that are superharmonic oo the central axis, we nd a general \pseudocon-cave" ordering of the ground state energies of the Hamiltonian restricted to the sectors with xed angular momentum. The physical applications include atoms and ions in strong magnetic elds. There the energies are monotone increasing and concave in angular momentum. In the case of a periodic chain of atoms the pseudoconcavity extends to the entire lowest band of Bloch functions.