Abstract
The Landau problem in non-commutative quantum mechanics (NCQM) is studied. First by solving the Schrödinger 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.
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Supported by National Natural Science Foundation of China (10465004, 10665001, 10575026) and Abdus Salam ICTP, Trieste, Italy