  We introduce new representations to formulate quantum mechanics on
noncommutative coordinate space, which explicitly display entanglement
properties between degrees of freedom of different coordinate components and
hence could be called entangled state representations. Furthermore, we derive
unitary transformations between the new representations and the ordinary one
used in noncommutative quantum mechanics (NCQM) and obtain eigenfunctions of
some basic operators in these representations. To show the potential
applications of the entangled state representations, a two-dimensional harmonic
oscillator on the noncommutative plane with both coordinate-coordinate and
momentum-momentum couplings is exactly solved.
