  We study the energy levels of a single particle in a homogeneous magnetic
field and in an axially symmetric external potential. For potentials that are
superharmonic off the central axis, we find a general ``pseudoconcave''
ordering of the ground state energies of the Hamiltonian restricted to the
sectors with fixed angular momentum. The physical applications include atoms
and ions in strong magnetic fields. 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.
