Project 1: Spin wave packet time evolution

Inject a spin-polarized (along the direction of motion) Gaussian wave packet into a quantum wire with Rashba spin-orbit interaction, modeled on the lattice 20x100 with tight-binding represented SO Hamiltonian, and evaluate how the Bloch vector of such electron changes as the packet traverses the wire. This requires to trace the full (pure) state density matrix of the packet at each instant of time over the orbital degrees of freedom and, thereby, obtain the reduced (spin) density matrix as a function of time.