“…The motivation for this kind of theory is that in the low energy effective theory of D-brane with a background magnetic field and an extreme situation such as in the string scale or at very high energy levels, not only the space noncommutativity may appear, but also the effects of momentum noncommutativity can be signi-ficant, which is called NC phase space. Hence, a lot of specific problems have been investigated on the theory of NC spaces such as the quantum Hall effects [8,9], the harmonic oscillator [10][11][12], the Fock-Darwin system [13], the coherent states [14], the classical-quantum relation-ship [15], the motion of the spin-1/2 particle under a uniform magnetic field [16], the Dirac equation with a magnetic field in D [17] and with the time-dependent linear potential [18], etc. The main approach is based on the Weyl-Moyal correspondence which amounts to replacing the usual product by a star product in NC space [19].…”