- 00-457 Bernhard Baumgartner, Robert Seiringer
- On the ordering of energy levels in homogeneous magnetic fields
Nov 17, 00
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Abstract. 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.