Analytic propagators for systems with spin-orbit-type interactions

We discuss propagators in spin-orbit-type systems. In addition to the kinetic energy, these systems exhibit potentials that mix position, momentum and spin operators. We give analytic expressions for propagators for constrained spin-orbit coupling Hamiltonians $H=\frac{\textbf{p}^2}{2m}+f(\textbf{x},\textbf{p},\sigma)+\frac{1}{2}m\eta^2 (x^2+y^2)$ for some specific functions $f$. We discuss the applicability of two propagator construction methods and we obtain the evolution of particles with spin.