Time evolution of a detected particle

[hokhani]

TL;DR

What is the time evolution of a quantum particle which is already detected at a point?

Suppose that we detect a quantum particle at the position $x_0$. Then, we would like to know about its position at a next time. Does the particle stay at $x_0$ while the detector is turned on?

 

[anuttarasammyak]

No. Uncertainty of momentum is infinite so the particle has almost light speed. Furthermore particle anti particle pairs with similar speed are created by precise measurement of position which requires high energy. We will not be able to distinguish which particle is our own among these dispersing anti particle particle juice.