On the ordering of energy levels in homogeneous magnetic fields

Details On the ordering of energy levels in homogeneous magnetic fields On the ordering of energy levels in homogeneous magnetic fields

2000-11-17

arxiv.org/abs/math-ph/0011031v1

Lett. Math. Phys. 54, 213 (2000)

Physics

Mathematical Physics

LaTeX2e, 14 pages

Scientific paper

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.

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