  A basic problem in the relativistic quantum Hamilton-Jacobi theory is to
understand whether it may admit superluminal solutions. Here we consider the
averaging of the speed on a period of the oscillating term which is similar to
Dirac's averaging of the oscillating part of the free electron's speed. Such an
averaging solves the problem of getting the $\hbar\to 0$ limit of the speed of
the free particle, and leads to solutions that, depending on the integration
constants, may be superluminal.
