Angular velocity operator and q-deformation structure

We present the definition of the angular velocity in quantum mechanics. To accomplish this, first we show that quantum-mechanical description of rotation angles proposed by Barnett and Pegg [Phys. Rev. A 41, 3427 (1990)] (the BP formalism) possesses a q-deformation structure inherently in itself. Based on this idea, we then construct the angular velocity operator via the q-deformed Heisenberg equation of motion. It is found that this operator exhibits a physically plausible behavior in the semiclassical regime of large angular momenta. This gives a resolution to the problem of anomalous properties of the angular velocity dynamically defined from the BP angle operator. We discuss in detail how the classical-quantum correspondence is established for the angular velocity variable if the q-deformation structure is introduced. Our result can also be seen as an example of the physical reality of the q-deformation prescription.