  The concept of the one -- dimensional quantum mechanics in the relativistic
configurational space (RQM) is reviewed briefly. The Relativistic Schroedinger
equation (RSE) arising here is the finite-difference equation with the step
equal to the Compton wave length of the particle. The different generalizations
of the Dirac -- Infeld -- Hall factorizarion method for this case are
constructed. This method enables us to find out all possible finite-difference
generalizations of the most important nonrelativistic integrable case -- the
harmonic oscillator. As it was shown (\cite{kmn},\cite{mir6}) in RQM the
harmonic oscillator = $q$ -- oscillator. It is also shown that the relativistic
and nonrelativistic QM's are different representations of the same theory.
Thetransformation connecting these two representations is found in explicit
form. It could be considered as the generalization of the Kontorovich --
Lebedev transformation.
