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It does not make sense to propose your "alternative HUP" without changing everything else about quantum mechanics, too. The uncertainty principle is not some sort of axiom of quantum mechanics, it is a direct consequence of the Robertson-Schrödinger relation, which holds generally for all observables on all Hilbert spaces. We cannot talk about ...

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A few years ago I read a book (might have been Thinking, Fast and Slow by Daniel Kahnemann) in which it was stated that the much better way to follow a lecture is to actually read the lecture notes before the lecture takes place and then to just pay attention during the lecture (and of course to ask questions). The worst method according to this book was ...

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First thing to note is that the available phase space for the new inequality is much smaller than the older one. This can be visualised in the following way. Here, the blue region is the phase space available due to the original HUP and the red region corresponding to the new UP is the complement of it. The old HUP imposed a lower bound on possible momentum ...

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Imagine an infinite well, so that $\sigma_x$ is clearly bounded. Then you would have a maximum on $\sigma_p$, which mean you could not construct arbitrary solutions as linear combos of the eigensolutions. For instance an initial state $(\psi_1(x)+\psi_n(x))/\sqrt{2}$ would have a maximum value of $n$ else $\sigma_p$ would be “too large”. Hence some linear ...

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There are some problems with the "reversed" Heisenberg principle you are mentioning. It just does not makes sense in the frame of standard QM. Hand wavy physical argument: First of all, since the product $\sigma_x \sigma_p$ is interpreted as an area in phase-space (or configuration-space) it would include the case where this area is zero, which (...

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