  One of the simplest example of non-commutative (NC) spaces is the NC plane.
In this article we investigate the consequences of the non-commutativity to the
quantum mechanics on a plane. We derive corrections to the standard
(commutative) Hamiltonian spectrum for hydrogen-like atom and isotropic linear
harmonic oscillator (LHO) and formulate the problem of the potential scattering
on the NC plane. In the case of LHO we consider the noncommutativity of the
momentum operators, too.
