  We study evolution of a quantum particle in a harmonic potential whose
position and momentum are repeatedly monitored. A back-action of measuring
devices is accounted for. Our model utilizes a generalized measurement
corresponding to the Positive Operator-Valued Measure. We assume that upon
measurement the particle's wavefunction is projected onto one of possible
detector states depending on the observed result. We chose these
post-measurement states to be moving Gaussian wavepackets. The Wave Function
Quantum Monte-Carlo formalism is used to simulate single quantum trajectories
of the particle. We show how classical trajectories emerge in course of
observation and study in detail dispersion of position and momentum of the
particle.
