Transport and scattering phenomena in open quantum-systems with a continuous energy
spectrum are conveniently solved using the time-dependent Schrödinger equation. In the timedependent
picture, the evolution of an initially localized wave-packet reveals the eigenstates and
eigenvalues of the system under consideration. We discuss applications of the wave-packet method
in atomic, molecular, and mesoscopic systems and point out specific advantages of the timedependent
approach. In connection with the familiar initial value formulation of classical mechanics,
an intuitive interpretation of transport emerges. For interacting many-particle systems, we discuss
the efficient calculation of the self-consistent classical transport in the presence of a magnetic field.