Angular momentum of a relativistic wave packet

Abstract

Quantum-mechanical spin is often thought of in terms of classical angular momentum. In fact spin is defined by its commutation relations and the spin and orbital angular momentum operators are very different. Here we solve the Dirac equation in a rotating frame of reference and create a localized wave packet from the resulting wave functions to examine the consequences of the rotational motion. We highlight some unexpected effects in the properties of the wave packet and show that the spin operator and orbital angular momentum operator describe different aspects of the rotational properties of the wave packet. It is also observed that neither quantum-mechanical spin nor orbital angular momentum can be fully understood within an inertial frame.