This research presents a stochastic Schrödinger equation that describes continuous measurement outcomes for position and momentum, highlighting implications for understanding quantum states.
A stochastic Schrödinger equation is presented to describe simultaneous continuous measurement of the position and momentum of a non-relativistic particle. The equation is solved to yield a state localised in position and momentum contingent on the uncertainty principle. The state is understood as that to which the particle tends after a period of continuous measurement. The solution takes the form of a wave packet of fixed Gaussian shape whose centre undergoes random motion in phase space. It is shown to be locally stable.
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Daniel Bedingham (2025) studied this question.
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