Manyetik alan ve çeşitli potansiyeller içeren dirac denkleminin tam ve yaklaşık çözüm

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