Quantum trajectories

A quantum trajectory represents a single history of the state vector of an open quantum system. The stochastic nature of its evolution can be viewed a s resulting from the quantum probabilities for the outcomes of measurements performed on the bath. We derive stochastic Schrodinger equations for vari ous trajectory models, starting from the full Schrodinger equation for the system and the bath combined. The state reduction of the bath at a measurem ent also projects the state of the system on a pure state, thereby destroyi ng the entanglement. The master equation for the system's density matrix is obtained as a result of the discussion, and it is not taken as its startin g point. The general concepts are illustrated in the specific case of an at om coupled to the radiation field.