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This work is mainly based on some theoretical surveys on two dimensionalquantum gravitational well, considering harmonic oscillator potential causes aneffective plank constant. We find that there is a similarity between twodifferent cases, potential free and oscillator potential in noncommutativephase space in commutative momentum, but in noncommutative, non zero space andmomentum The Hamiltonian would a little bit different in energy levels.

Noncommutative Simple Harmonic Oscillator in Quantum Gravitational Well