  We calculate the propagator of a particle caught in a Paul trap and subject
to the continuous quantum measurement of its position. The probabilities of the
measurement outputs, the possible trajectories of the particle, are also found.
This enables us to propose a series of experiments that would allow to confront
the predictions of one of the models that describe the interaction between a
measured quantum system and measuring device, namely the so called Restricted
Path-Integral Formalism, with the experiment.
