Analytic propagators for spin-orbit interactions

We derive analytic expressions for propagators in spin-orbit coupled systems. In addition to their kinetic energy, these systems exhibit a potential energy that mixes position, momentum and spin operators. We consider Hamiltonians with limited noncommutativities: the confined spin-orbit coupled Hamiltonian, the confined Equal-Strength-Rashba-Dresselhaus Hamiltonian and the confined Opposite-Strength-Rashba-Dresselhaus Hamiltonian. We use both a classical action method and an algebraic method in our derivations. We mention specific applications for these propagators and illustrate their significance with examples of wavepacket evolution.