Position measurements are examined under the assumption that object position X?_ι and probe position X?_ι just after the measurement are expressed as a linear combination of positions x?_o and x?_o just before the measurement. The Heisenberg uncertainty relation between the position uncertainty and momentum disturbance holds when the measurement error ∈(x_t) for the object position x?_ι is adopted as the position uncertainty. However, the uncertainty in the measurement result obtained for x?_o is the standard deviation of the measurement result, and not the measurement error ∈(x_o). This difference is due to the reduction of a wave packet. The validity of the linearity assumption is examined in detail.
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