What is a practical experiment in which the position of a quantum particle is measured? What is the most simple/basic way to measure the position of a quantum particle? How does this experiment work exactly?
 A: The double slit experiment is typically described as passing a photon or electron through a double slit and letting it hit a screen. A cathode ray tube is an example of this type of screen. The inside of a glass tube is coated with phosphor. An electron hits an atom on the screen, which gives off light. You can see the position of the light.
On electron gives on flash. But if you repeat this experiment many times, the flashes add up to an interference pattern.
You can measure any electron and get a precise measure of its position, to the size of an atom.
The uncertainty principal prevents you from predicting which atom an electron will hit. You can predict the position as precisely as the interference pattern.
In a real old-fashioned television you do not put a double slit in the CRT. The electron is emitted from a small hot wire and given as low a transverse velocity as possible. The uncertainty in the position and momentum as it leaves the wire is not necessarily as small as the uncertainty principal would permit. It might be larger because of the size of the wire, imperfectly controlled voltages, and so on. Never the less, it is sufficiently precise that it can be steered to hit a small spot on the screen.
A: The simplest setups that come to my mind:

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*Any photomultiplier tube (PMT) in a dark box with a dim light diode (LED). When you see a signal of the right size, you know a photon has hit its photocathode.

*A Geiger tube. When it clicks, you know a particle was in it.

