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 H-SO(c) = p(2)/2m + gamma sigma . L + 1/2m eta(2)(x(2) + y(2)), the confined Equal-Strength-Rashba-Dresselhaus Hamiltonian H-ESRD(c) = p(2)/2m + alpha/(h) over bar (p(x) + p(y))(sigma(x) - sigma(y)) + 1/2m eta(2)(x(2) + y(2)) and the confined Opposite-Strength-Rashba-Dresselhaus Hamiltonian H-OSRD(c) = p(2)/2m + alpha/(h) over bar (p(x) - p(y))(sigma(x) + sigma(y)) + 1/2m eta(2)(x(2) + y(2)). 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.