  In this study, the Majorana equation for particles with arbitrary spin is
solved for a half-integer spin free particle. The solution for the fundamental
state, corresponding to the reference frame in which the particle is at rest,
is compared with that obtained using the Dirac equation, especially as regards
the approximation in the relativistic limit, in which the speed of the particle
is close to that of light. Furthermore, the solutions that Majorana defines
unphysical, proving that their occupation probability increases with the
particle velocity, are taken into consideration. The anomalous behavior
exhibited by these states also shows that for high-energy particles with small
mass, transitions from a bradyonic state to a tachyonic state become possible.
