  Quantum transport in a lattice is distinct from its counterpart in continuum
media. Even a free wave packet travels differently in a lattice than in the
continuum. We describe quantum scattering in a one dimensional lattice using
three different formulations and illustrate characteristics of quantum
transport such as resonant transmission. We demonstrate the real time
propagation of a wave packet and its phase shift due to impurity
configurations. Spin-flip scattering is also taken into account in a spin chain
system. We show how individual spins in the chain evolve as a result of a
spin-flip interaction between an incoming electron and a spin chain.
