Abstarct: In this thesis, We study the relativistic and non-relativistic equation in commutative, non-commutative space and phase space with different potential under magnetic field hence the other choice is studying the equations in absence of magnetic field. We obtain energy spectrum and wave function in different situations by NU method. Also, we studied the Dirac oscillator problem in the presence of a harmonic interaction in both commutative and non-commutative cases. The motivation behind our study was the outstanding role of Dirac oscillator, harmonic interaction and the external magnetic field in particle and high-energy physics. We showed that the problem can be simply solved in an exact analytical manner by using proper transformations and the NU technique. As we expect, the results of the NC space, in the limit θ→0 yield the commutative analogues. As the exact relations for the energies and the eigenfunctions are presented, the results can be immediately used to investigate the binding energies and many static properties. We can see that the effect of the NC parameter on the Landau levels is not negligible. It is also observe for relativistic bosons that when the quantum number change from n=1, λ=0 to n=3, λ=2, the energy eigenvalues decrease in the both spaces. It is easy to show that we recover the case of commutative space as a special case of NC space by taking θ = 0. We calculated spectrum of energies of relativistic fermions with spin 1/2 for different n, l that related to the relativistic Dirac oscillator under a magnetic field, that the effect of the NC parameters on landau levels is considerable that compared with when the noncommutative parameters are zero. In fact, for the system will behave like the landau problem in commutative space., i.e. the normal Zeeman effect. We see that for the case of equal scalar and vector potentials in commutative space, the system becomes more bounded for increasing quantum numbers n and l. On the contrary, in the NC space, the system becomes more excited for increasing quantum numbers. In addition, it is observed that the energy difference between the neighbor states becomes less in the NC space.