Topological Changes of Wave Functions Associated with Hamiltonian Monodromy

Almost everything that happens in classical mechanics also shows up in quantum mechanics when we know where to look for it. A recently discovered phenomenon in classical mechanics involves topological changes in the loops that define action and angle variables as a result of a passage around a ``monodromy circuit''. This phenomenon is known by the short name ``Hamiltonian monodromy'' (or, more ponderously, ``nontrivial monodromy of action and angle variables in integrable Hamiltonian systems''). In this paper, we show a corresponding change in quantum wave functions: these wave functions change their topological structure in the same way that the action and angle loops change.