Quantum trajectories generalized

By definition, an ensemble of quantum trajectories reproduces the density m atrix of an open system after ensemble averaging. We present a general clas s of stochastic Schrodinger equations for quantum trajectories which unifie s and extends existing methods. Various quantum jump and state-diffusion me thods are recognized as opposite limiting cases. The inherent freedom of ch oice can be used to significantly reduce the calculation time in specific c ases. Examples of this are methods with adaptive noise, for which a specifi c observable becomes noise free to first order. Linear stochastic equations can also be constructed, which allow analytical solutions. As an illustrat ion, the decoherence of Schrodinger cat states of a cavity mode is discusse d.