  A derivation of stochastic Schrodinger equations is given using quantum
filtering theory. We study an open system in contact with its environment, the
electromagnetic field. Continuous observation of the field yields information
on the system: it is possible to keep track in real time of the best estimate
of the system's quantum state given the observations made. This estimate
satisfies a stochastic Schrodinger equation, which can be derived from the
quantum stochastic differential equation for the interaction picture evolution
of system and field together. Throughout the paper we focus on the basic
example of resonance fluorescence.
