  We present a formalism that accounts for the evolution of quantum states of
travelling light pulses incident on and emanating from a local quantum
scatterer such as an atom or a cavity. We assume non-dispersive asymptotic
propagation of the pulses and Markovian coupling of the stationary system to
input and output fields. This permits derivation of a cascaded system master
equation where the input and output pulses are treated as single oscillator
modes that both couple to the local system. As examples of our theory we
analyse reflection by an empty cavity with phase noise, stimulated atomic
emission by a quantum light pulse, and formation of a Schr\"odinger-cat state
by the dispersive interaction of a coherent pulse and a single atom in a
cavity.
