Solutions of the Dirac Equation in the Presence of a Uniform Back-Ground Magnetic Field
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Date
2009-06
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Addis Ababa University
Abstract
This thesis which is entitled as ”Solutions of the Dirac Equation in the Presence of
a Uniform Back-ground Magnetic Field” tried to find exact solutions of the Dirac
equation under the assumption of some gauge conditions and taking the field as a
uniform field. Since theoretical evidences indicates that most of the bodies in our
universe posses a complicated magnetic field, we need to find the solutions of the
Dirac equation in the presence of this field, by assuming the field as being uniform.
To do this we began by considering the Dirac equation and we tried to find its exact
solution. To find the exact solutions, we used a gauge condition,
~A
= Axi = −yBi
where B is the magnitude of the magnetic field. In addition some quantum mechanical
concepts was used. Once the Dirac equation is exactly solved, we can proceed to
calculate elementary particle decays and scattering cross-sections in the presence of a
magnetic field. In this thesis particularly we focussed on the nature of the solutions
of the Dirac equation in the presence of a uniform magnetic field and orthogonality
relations
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Solutions of the Dirac Equation