Propagators for Hamiltonians with Spin-Orbit Coupling

Quantum mechanical propagators can be used to understand the dynamics of electrons in confined electromagnetic environments. We extend the propagator formalism to include the spin degree of freedom for spin-orbit coupling potentials~in two-dimensional geometries.~The 2x2 spin propagators allow us to follow the evolution in time and space of the spin-components of localized wave packets. We apply the technique to Rashba and Dresselhaus interactions and present graphical displays of the corresponding spin motions.~