The quantum state diffusion model describes the evolution of an individual open quantum system by an Itô diffusion equation. In this paper we show two examples of open systems which can be analytically treated, the damped harmonic oscillator and a pumped two-level system with spontaneous emission. The coherent states of the oscillator remain coherent through the stochastic evolution and undergo a classical Ornstein-Uhlenbeck process. We also consider time correlation spectra of the solutions of these stochastic equations.
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