  We derive the stochastic Schrodinger equation for the limit of continuous
weak measurement where the observables monitored are canonical position and
momentum. To this end we extend an argument due to Smolianov and Truman from
the von Neumann model of indirect measurement of position to the Arthurs and
Kelly model for simultaneous measurement of position and momentum. We only
require unbiasedness of the detector states and an integrability condition
sufficient to ensure a central limit effect. Despite taking a weak interaction,
as opposed to weak measurement limit, the resulting stochastic wave equation is
of the same form as that derived in a recent paper by Scott and Milburn for the
specific case of joint Gaussian states.
