  The paper explores quantum mechanics of half-spin particle motion in the
field of Reissner-Nordstroem (RN) naked singularity. It is shown that for any
quantum mechanical Dirac particle, irrespective of availability and sign of its
electrical charge, the RN naked singularity is separated by an infinitely high
positive potential barrier. With like charges of a particle and the source of
the RN naked singularity, near the origin there exists the second completely
impenetrable potential barrier. It has been proved that in the field of the RN
naked singularity, bound states of half-spin particles can exist. The
conditions for appearance of such states were revealed and computations were
performed to find energy eigenvalues and eigenfunctions.
