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Abstract:
This thesis examines the dynamics of electrons in a gravitational plane wave. To this end, a plane wave solution to the Dirac equation for an electron in a gravitational plane wave is first presented. A comparison of this solution with the ”Volkov state” not only demonstrates that electrons behave almost identically as in a electromagnetic plane wave, but also enables the assignment of a generalized ”vector potential” −Hiμ to the gravitational wave, which couples to the initial kinetic momentum μ rather than to the mass. Furthermore, a solution to the Dirac equation for an electron vortex beam in a gravitational plane wave is constructed, that is, a solution with orbital angular momentum (OAM). In contrast to the plane wave solutions, this solution differs from that of a vortex beam in an electromagnetic plane wave, which is primarily due to the coupling of the generalized ”vector potential” −Hiμ to the initial kinetic momentum pμ. Finally, a spinor is presented that represents a solution to the classical equivalent of the Dirac equation for a particle in a gravitational plane wave. The comparison with the plane wave solution to the Dirac equation reveals that the dynamics can also be accurately described by the classical spinor.
