Square billiard with an Aharonov–Bohm flux line

Explicit formulas for the eigenstates and energy levels of a square quantum billiard with an Aharonov–Bohm flux line are found in quasiclassical approximation, that is, for high enough energy. There are localized states, never before noticed in this well studied problem, whose localization is due to phase interference, even though there is no classical effect of the magnetic flux.