  We obtain exact solutions of the 2D Schr\"odinger equation for Hydrogen atom
with the lenear and Harmonic Potentials in noncommutative complex space, using
the Power-series expansion method. Hence we can say that the Schr\"odinger
equation in noncommutative complex space describes to the particles with spin
(1/2)in an external uniform magnitic field. Where the noncommutativity play the
role of magnetic field with created the total magnetic moment of particle with
spin 1/2, who in turn shifted the spectrum of energy. Such effects are similar
to the Zeeman splitting in a commutative space.
