The Solution Of The Dirac Equation In3D Non-commutative Phase Space

In this thesis, we propose the operator method to analyze the spectra and wave functions of Dirac equation with a magnetic field in3D non-commutative phase space. The contents of this thesis are the following:1) A whole review was made on the basic nature of the Dirac equation and the non-commutative (phase) space.2) For a spin-1/2particle moving in a background magnetic field in non-commutative phase space, Dirac equation is solved when the particle is allowed to move off the plane that the magnetic field is perpendicular to. It is shown that the motion of the charged particle along the magnetic field has the effect to increase the magnetic field. In the classical limit, matrix elements of the velocity operator related to the probability give a clear physical picture: Along an effective magnetic field the mechanical momentum is conserved and the motion perpendicular to the effective magnetic field follows a round orbit. If using the velocity operator defined by the coordinate operators, the motion becomes complicated.