This work revisits the apparent paradox that emerges from some results found in many basic textbooks
which address the problem of calculating the phase velocity of free particles in the relativistic
regime and its relation with the same quantity in the non-relativistic regime. Because some books
use the Newtonian kinetic energy and others use the total relativistic energy (including the rest
energy), the non-relativistic limit of the relativistic phase velocity differs from the Newtonian
phase velocity, which can be confusing for many students. This paper proposes expressing the phase
velocity by first subtracting the rest energy from the relativistic energy before imposing the usual
de Broglie relations. In addition to providing the corresponding Newtonian phase velocity, it also
provides a relativistic Schrödinger equation which intuitively reduces to the non-relativistic
Schrödinger equation in the appropriate regime. The problem of the equivalence between the
relativistic Sc…