Abstarct: The noncommutative space can be considered as extension of the commutative space so that commutation relation between the operators is expressed by the changed heisenberg algebra. In order to conforming between theoretical and experimental datas on phenomena such as hall effect and eliminating divergence values created in field theory, noncommutative space would be introduced. We investigate in this frxame the effect of noncommutative parameters on physical systems such as free particle, harmonic oscillator, quantum hall effect and three body systems. We study Wigner distribution function as quantum distribution function in the phase space which expresses the probability distribution of the position and momentum simultaneously ( also it is’nt contradiction with the hiesenberg uncertainty principle). So using the wigner distribution function we can compare the classical and quantum mechanics, since both of them are expressed in a same space. Finally with the introduction of dynamic invariant approach we discuss on the time- dependent problems in the noncommutative space.