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What is the physical meaning of Heisenberg's Uncertainty Principle? We have derived it mathematically but what is the logical explanation for it?

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A wave packet is localized in space, but it is a superposition of many waves of different wavelengths.

A simple wave has a distinct wavelength, but it is spread out in space.

The wavelength corresponds to the momentum of a particle: $p = \frac{h}{\lambda}$.

These are examples where you can't know both the position and wavelength (i.e., momentum) of a wave form.

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