Exact, and approximate solutıon of the dirac equation in the presence of the magnetic field with various potentials

Abstract

Dirac equation has been studied for many years and its role in modelingphysical problems is well known. In particular, Dirac equation is useful to describeproperties of the spin 1/2 particles. Therefore the study of the Diracequation has considerable impact on physics.On the other hand the study of position dependent mass Schr¨odinger equationhas recently attracted some interest arising from the study of the electronicproperties of the semiconductors, quantum dots etc.In this thesis, the solution of the Dirac equation and transmission probabilitiesof the scattering problem with a position dependent mass are studied.Thus this work consists of two parts. In the first part, exact solvability of theposition dependent mass Schr¨odinger equation including a constant potential hasbeen discussed and calculations of the transmission coefficients for various spatiallyvarying effective masses have been represented. The second part covers theconstruction and solution of the Dirac equation including various potentials inthe presence of the magnetic field. The ultimate goal of the models developed inthis thesis is that the solution of the effective mass Dirac equation with constantpotential.Key words: Dirac equation, (Quasi) exactly solvable potentials