Evolution Law of Quantum Observables from Classical Hamiltonian in   Non-Commutative Phase Space
  The evolution equations of quantum observables are derived from the classical Hamiltonian equations of motion with the only additional assumption that the phase space is non-commutative. The demonstration of the quantum evolution laws is quite general; it does not rely on any assumption on the operator nature of x and p and is independent of the quantum mechanical formalism. 
Daniela Dragoman