Re-Thinking Schroedinger Boundary Conditions: the Simple Rotator is Not   Simple
  A contradiction arises when applying standard boundary conditions to a simple quantum rotator with a single coordinate. New boundary conditions for the Schroedinger equation are proposed that involve only gauge invariant quantities, and that can be applied beyond the immediate problem. The use of gauge invariant boundary conditions has important consequence for energy flow in or out of a simple rotator. 
Arthur Davidson