Abstract

The path-integral theory of quantum continuous measurements is applied to monitoring linear momentum. It is shown that conservation of linear momentum may be verified by such a measurement with any accuracy. The force acting on a particle can be arbitrarily accurately estimated from the output of the measurement provided that the measurement error is made sufficiently small. This is characteristic for a quantum nondemolition (QND) measurement. The results of this analysis are discussed in the context of the energy-time uncertainty relation.

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