Square billiard with a magnetic flux
Eigenstates and energy levels of a square quantum billiard in a magnetic field, or with an Aharonov-Bohm flux line, are found in quasiclassical approximation, that is, for high-enough energy. Explicit formulas for the energy levels and wave functions are found. A number of interesting states are shown, together with their wave functions. Some states are diamagnetic, others paramagnetic, still others both dia- and paramagnetic. Some states are strongly localized. Related systems and possible experiments are briefly mentioned.
Narevich
R
Department of Physics, University of Maryland, College Park, Maryland 20742 and Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506, USA.
Prange
RE
Zaitsev
O