Approximations to Relativistic Quantum Theory in the Non-Relativistic Regime

When studying quantum dynamics in the non-relativistic regime, the convention is to use non-relativistic quantum theory instead of the more accurate relativistic quantum theory as it is always assumed to be a good approximation. Therefore, this thesis examines how well this approximation, as well as the use of an ensemble of relativistic classical trajectories, are to relativistic quantum theory in the non-relativistic regime. Evaluating the breakdown of agreement of these approximations to relativistic quantum theory in the non-relativistic regime would have applications in many fields of physics (ranging from atomic to molecular, chemical, and condensed-matter physics) and engineering.