Solutions Of The Dirac Equation In The Presence Of A Uniform Back-ground Magnetic Field

This thesis which is entitled as ”Solutions of the Dirac Equation in the Presence ofrna Uniform Back-ground Magnetic Field” tried to find exact solutions of the Diracrnequation under the assumption of some gauge conditions and taking the field as arnuniform field. Since theoretical evidences indicates that most of the bodies in ourrnuniverse posses a complicated magnetic field, we need to find the solutions of thernDirac equation in the presence of this field, by assuming the field as being uniform.rnTo do this we began by considering the Dirac equation and we tried to find its exactrnsolution. To find the exact solutions, we used a gauge condition,rn~Arn= Axi = −yBirnwhere B is the magnitude of the magnetic field. In addition some quantum mechanicalrnconcepts was used. Once the Dirac equation is exactly solved, we can proceed torncalculate elementary particle decays and scattering cross-sections in the presence of arnmagnetic field. In this thesis particularly we focussed on the nature of the solutionsrnof the Dirac equation in the presence of a uniform magnetic field and orthogonalityrnrelations

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