  The Landau problem in non-commutative quantum mechanics (NCQM) is studied.
First by solving the Schr$\ddot{o}$dinger equations on noncommutative(NC) space
we obtain the Landau energy levels and the energy correction that is caused by
space-space noncommutativity. Then we discuss the noncommutative phase space
case, namely, space-space and momentum-momentum non-commutative case, and we
get the explicit expression of the Hamiltonian as well as the corresponding
eigenfunctions and eigenvalues.
