Noncommutative Simple Harmonic Oscillator in Quantum Gravitational Well
  This work is mainly based on some theoretical surveys on two dimensional quantum gravitational well, considering harmonic oscillator potential causes an effective plank constant. We find that there is a similarity between two different cases, potential free and oscillator potential in noncommutative phase space in commutative momentum, but in noncommutative, non zero space and momentum The Hamiltonian would a little bit different in energy levels. 
Farhad Zekavat
quant-ph