  The main point of this paper is to examine a "hidden" dynamical symmetry
connected with the conservation of Laplace-Runge-Lenz vector (LRL) in the
hydrogen atom problem solved by means of noncommutative quantum mechanics
(NCQM). The basic features of NCQM will be introduced to the reader, the key
one being the fact that the notion of a point, or a zero distance in the
considered configuration space, is abandoned and replaced with a "fuzzy"
structure in such a way that the rotational invariance is preserved. The main
facts about the conservation of LRL vector in both classical and quantum theory
will be reviewed. Finally we will search for an analogy in the NCQM, provide
our results and their comparison with the QM predictions. The key notions we
are going to deal with are non-commutative space, Coulomb-Kepler problem and
symmetry.
