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my concern is, that there is a huge amount of equations that are somehow related to the uncertainty principle and it is not straightforwardly obvious to me, when i have to use which of them.

let me put it this way: as far as i see, there is this overall applicable equation that says

ΔxΔp ≥ h/(4π)

but for instance, my schoolbook proposes the relation ΔxΔp=h/2, when they talk about the uncertainty of a single slit diffraction pattern that is made with electrons, where they regard Δx as half the slit-width and Δp as the x-deflection of the electron in units of momentum, that it needs to reach the first minimum. it appears to me, that this approach is extremely arbitrary and now there are lots of excercises, where they e.g. say that by using light, Δx is half the coherence length of light and use the same relation.

and now i found an excercise, where they assume that the uncertainty of an electron in a hydrogen atom is about 10^(-10) m, and ask for the uncertainty in momentum.

the solution to this excercise is easily derived from the assumption that ΔxΔp≈h<---but where does this come from? how do i get this?

so my question is, how do i find the appropriate relation to the given problem?

sorry about my english...

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# Uncertainty principle and single slit experiment

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