Suppose, a particle has non zero probability to be in any between x = 1 and x = 10. Let, we measure its position with a very low energy photon. It will collapse it’s wave function, since it disturbs the system.
What will be the result of such an experiment? Will the position of the particle be determined as a large range, like between x = 4 and x = 7, or it will be a random value of a very small range between 4 and 7 (like 5.1-5.2)? I am a bit confused here. The wave function collapses, but we are measuring with a very imprecise device (a very low energy photon).
What will determine its momentum uncertainty? The range between 4 and 7? Or it will be almost completely indeterminant (in case the position we measured is actually a random value with a tiny range)?
Any help will be appreciated.