February 2, 2022 Thesis Open Access

ALEMAYEHU NEGERA WAKWOYA

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    <subfield code="a">SOLUTION OF DIRAC EQUATION IN ELECTRIC, MAGNETIC AND  ORTHOGONAL ELECROMAGNETIC FIELD</subfield>
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    <subfield code="a">&lt;p&gt;ADVISOR: Dr. AJAI KUMAR MISHRA&lt;/p&gt;

&lt;p&gt;ABSTRACT&lt;/p&gt;

&lt;p&gt;In the present work, the solution of Dirac equation in electric, magnetic and orthogonal electromagnetic field was investigated. The corresponding magnetic field has been evaluated by swapping the role of known and unknown quantities. Solving the Dirac equation with space-time-dependent potentials is crucial for the understanding of pair creation due to the Sauter-Schwinger effect. Only few exact solutions are known today, but no solutions have been established where the electric field does depend on more than one space-time coordinate.A method for generating solutions of the Dirac equation in the presence of space-time-dependent electromagnetic fields has been developed. By swapping the roles of known and unknown quantities in the Dirac equation, we are able to choose arbitrary solutions and calculate the corresponding electromagnetic field. Either using the present method solutions with an electromagnetic field depending on one of the light cone coordinates or both can be found in (1+1) dimensions. By choosing a specific ansatz, it is possible to formulate conditions for solutions that correspond to perturbative paircreation.&lt;/p&gt;

&lt;p&gt;Key words: Dirac and Klein-Gordon equations, Electric field&lt;/p&gt;</subfield>
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