Scattering and bound states of dirac particles in an external field

In order to understand the nature of basic particles, the Dirac equation has been studied for many years. The Dirac equation plays an important role in well known modelling physical problem. Additionally, to describe properties of the spin 1/2 particles, the Dirac equation is a useful one, so one can consider the solution of Dirac equation is important in physics. Furthermore, the study of Dirac equation including various potentials like harmonic oscillator potential, Coulomb potential, Rosen-Morse potential etc. has recently attracted interest on physical systems. In this thesis, in the presence of exactly solvable potential and an external magnetic field, the Dirac equation has been studied for scattering and bound states. Because of that this work consists of three parts. In the first part the Dirac equation is generally solved for free particles and existing various potentials. The scattering of a Dirac particle is studied in the external magnetic field in the second part. As in the last part, the bound state of Dirac particle is investigated. The ultimate goal of the study in this thesis is defining the scattering and bound states of Dirac particles in an external field.