  The von Neumann interaction between a particle and an apparatus has been
considered in the measurement of the position of a particle when the
interaction lasts for a finite amount of time. When the measurement has finite
duration, both the motion of the pointer and the particle influence the result
of the measurement. Provided that the particle is in an eigenstate of its
position at the start of the measurement, the pointer will indicate the
arithmetic average between the initial and final position of the particle.
Furthermore, the probability that the pointer will indicate a given average
value is equal to the transition probability for the undisturbed particle to
experience the change in position. If the initial state of the pointer is a
narrow wavepacket, then for any initial state of the particle, the measurement
yields, approximately, the undisturbed probability distribution for the
position of the particle at the end of the measurement.
