It's fairly common for people to relate this quantum phenomenon to the uncertainty principle, though. Someone asks: "Why can't I just say 'the particle is at re

It's fairly common for people to relate this quantum phenomenon to the uncertainty principle, though. Someone asks: "Why can't I just say 'the particle is at rest in this small area' and expect it to stay there forever?" And one take on the answer is "Because you're imposing a very small uncertainty on the initial position, the initial momentum must have a very high uncertainty. That means there's a substantial probability that the particle will move away from its initial position over time, which corresponds to the wave function spreading out." You can certainly talk about it in terms of Fourier components or that sort of thing, too. There's a degree to which the uncertainty principle as applied to the position/momentum degrees of freedom is nothing but a statement about Fourier transforms. But I don't think it's a bad conceptual shorthand, especially for students who aren't yet experts in thinking about Fourier stuff.