  The framework of the relativistic quantum mechanics on spatially flat FLRW
space-times is considered for deriving the analytical solutions of the Dirac
equation in different local charts of these manifolds. Systems of commuting
conserved operators are used for determining the fundamental solutions as
common eigenspinors giving thus physical meaning to the integration constants
related to the eigenvalues of these operators. Since these systems, in general,
are incomplete on the FLRW space-times there are integration constants that
must be fixed by setting the vacuum either as the traditional adiabatic one or
as the rest frame vacuum we proposed recently. All the known solutions of the
Dirac equation on these manifolds are discussed in all details and a new type
of spherical waves of given energy in the de Sitter expanding universe is
reported here for the first time.
