  This paper provides an examination of how are prediction of standard quantum
mechanic (QM) affected by introducing a noncommutative (NC) structure into the
configuration space of the considered system (electron in the Coulomb potential
in the present case). The parameter controlling the extent of modification is
denoted as {\lambda}. The coordinates in the NC space are realized via creation
and annihilation operators acting in an auxiliary Fock space, this one being
chosen in such a way that the rotational invariance of the system remains
intact also in NCQM. Analog of Schr\"odinger equation for hydrogen atom is
found and analytically solved, both for bound states and scattering. The exact
formulas for NC corrections are given. None of the NC predictions contradicts
experimentally verified QM results, since in the correspondence limit {\lambda}
-> 0 both QM and NCQM coincide. Highly surprising feature of the NC version is
the existence of bound states for repulsive potential at ultra-high energies.
However, these disappear from the Hilbert space in the mentioned limit. The
whole problem is solved also using a method analogous to that of Pauli. Besides
rotational invariance, the dynamical symmetry related to the conservation of NC
analog of Laplace-Runge-Lenz vector is being used and the results obtained this
way are in the full agreement with those given by "Schr\"odinger-like"
approach. The presented NC deformation of QM preserves all those mysterious
properties of the Coulomb system that made it a distinguished key-stone of the
modern physics.
