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 wavefunctions are found. A number of interesting states are shown, together with their wavefunctions. 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. 
R. Narevich (1,2), R. E. Prange (1), and Oleg Zaitsev (1) ((1) U. of   Maryland, College Park, (2) U. of Kentucky, Lexington)