  We employ the path integral approach developed in [29] to discuss the
(generalized) harmonic oscillator in a noncommutative plane. The action for
this system is derived in the coherent state basis with additional degrees of
freedom. From this the action in the coherent state basis without any
additional degrees of freedom is obtained. This gives the ground state spectrum
of the system. We then employ the exact renormalization group approach to show
that an equivalence can be constructed between this (noncommutative) system and
a commutative system.
