  Effects of noncommutativity are investigated in planar quantum mechanics in
the coordinate representation. Generally these issues are addressed by
converting to the momentum space. In the first part of the work we show
noncommutative effects in a Gaussian wavepacket through the broadening of its
width. We also rederive results on *-product of Gaussian wavepackets. In the
second part, we construct a "Master" model for a noncommutative harmonic
oscillator by embedding it in an extended space. Different gauge choices
leading to different forms of noncommutativity, (such as between coordinates
only, between momenta only or noncommutativity of a more general kind), can be
studied in a unified and systematic manner. Thus the dual nature of these
theories are also revealed.
