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arXiv · 2509.11832

Localised solution of stochastic Schr\"odinger equation describing simultaneous continuous measurement of position and momentum

Daniel J. Bedingham
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Abstract

A stochastic Schr\"odinger 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 J. Bedingham. 2025-09-15. Localised solution of stochastic Schr\"odinger equation describing simultaneous continuous measurement of position and momentum. https://arxiv.org/abs/2509.11832

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