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We derive the stochastic Schrodinger equation for the limit of continuousweak measurement where the observables monitored are canonical position andmomentum. To this end we extend an argument due to Smolianov and Truman fromthe von Neumann model of indirect measurement of position to the Arthurs andKelly model for simultaneous measurement of position and momentum. We onlyrequire unbiasedness of the detector states and an integrability conditionsufficient to ensure a central limit effect. Despite taking a weak interaction,as opposed to weak measurement limit, the resulting stochastic wave equation isof the same form as that derived in a recent paper by Scott and Milburn for thespecific case of joint Gaussian states.Comment: 15 pages, no figure

Continuous measurement of canonical observables and limit stochastic Schrödinger equations