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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.

  1. 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).

  2. 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.

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You speak of a "low energy" photon. This means the wavelength $\lambda$ of the photon is "large". How large depends on how low the energy, $\lambda=\hbar c/E$.

Now you have to detect your photon. But you cannot get a precision on the position of that photon better than up to one wavelength, so this gives you a measure of the uncertainty on the position of your particle. The more precision you want, the more energy you must give to your photon and the more you disturb your system.

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