Coherence and squeezing along quantum trajectories

We perform a detailed analysis of the behaviour of coherent and squeezed states undergoing the time evolution. We calculate the time dependence of expectation values of position and momentum in coherent and squeezed states (which can be interpreted as quantum trajectories in coherent and squeezed states) and examine how the coherence and squeezing is affected during the time development, calculating the time dependence of the position and momentum uncertainty. We focus our investigations on two quantum systems. First we consider the quantum linear system with the Hamiltonian quadratic in q and p variables. As the second system we consider the simplest quantum nonlinear system with the Hamiltonian quartic in q and p variables. We calculate the explicit formulae for the time development of expectation values and uncertainties of position and momentum in an initial coherent state.