  The method of nonequilibrium Greens functions allows for a spatial and
energetical resolution of the electron current in Quantum Cascade Lasers. While
scattering does not change the spatial position of carriers, the entire spatial
evolution of charge can be attributed to coherent transport by complex wave
functions. We discuss the hierarchy of transport models and derive the density
matrix equations as well as the hopping model starting from the nonequilibrium
Greens functions approach.
