Three Dimensional Non-Commutative Quantum Mechanics

In this paper we discussed the three dimensional non-commutative quantum mechanics. We considered the three dimensional non-commutative space with only space-space non-commutativity. We discussed two examples: One is a harmonic oscillator problem and another a Coulomb problem. We used the perturbation method to solve the harmonic oscillator problem in three dimensional non-commutative quantum space. Up to a first order we obtained an energy eigenvalue for this Hamiltonian. In a similar way we obtained an energy eigenvalue for the hydrogen atom model in the three dimensional non-commutative space with only space-space non-commutativity by using the perturbation method.