In this paper we construct a path integral formulation of quantum mechanics
on noncommutative phase-space. We first map the system to an equivalent system
on the noncommutative plane. Then by applying the formalism of representing a
quantum system in the space of Hilbert-Schmidt operators acting on
noncommutative configuration space, the path integral action of a particle is
derived. It is observed that the action has a similar form to that of a
particle in a magnetic field in the noncommutative plane. From this action the
energy spectrum is obtained for the free particle and the harmonic oscillator
potential. We also show that the nonlocal nature (in time) of the action yields
a second class constrained system from which the noncommutative Heisenberg
algebra can be recovered.Comment: 9 pages Late
