my question is regarding finding momentum from uncertainty principle (I was trying to find Bohr radius from UP).
We normally state the uncertainty principle as follows:
$$\Delta{x}\Delta{p}\geq \hbar/2$$
but while solving it for momentum, I have seen people simply drop the 1/2 and treat it as (for example, as one user mentioned in the comments here; How to get the radius of Bohr from the uncertainty principle?):
$$p\sim \hbar/x$$
And to my surprise, using this gives the correct answer instead of $h$ or $\hbar/2$. Could someone explain why do we use it and how to get this version?
