Quantum gears: a simple mechanical system in the quantum regime

The quantum mechanics of a simple mechanical system is considered. A group of gears can serve as a model for several different systems such as an artifically constructed nanomechanical device or a group of ring molecules. It is shown that the classical motion of the gears in which the angular velocities are locked together does not correspond to a solution of the quantum problem. The general solution for several gears is discussed and the correspondence to the classical behaviour established.