Square billiard with a magnetic flux

Abstract

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.