## Stability of Electron/Nucleus; Heisenberg Unc.

JK423:

What you're saying makes logical sense. It's just a bit different than what I had understood the words to mean. Yours is logical, just different...unless I am missing something.

You describe momentum here as something that is well-defined, just having a higher range of possible measurable values, thus shifting the average of whatever probability distribution function characterizes momentum, and THAT is the meaning of "uncertainty."

I assume when you say dispersion, you mean the same as uncertainty (I just normally associate "dispersion" as meaning a function which gives the frequency dependence of some property and keep using "uncertainty"; please let me know if that is problematic in some other way).

This is different than what I how I had always thought of it. I don't want to mis-represent Fourier or Griffiths...but my understanding of HUP is more akin to my readings of Fourier analysis and Griffiths QM book. To my understanding, Griffiths described HUP as a reflection of the idea that, below a certain scale of size, both of these variables don't have meaning. That makes physical sense to me; at some scale, you can't know the speed and position of a wave/particle, because a wave's "position" is irrelevant unless the packet is extremely localized, etc. This also makes sense to me in terms of Fourier analysis: anything obeying the wave equation, mathematically, obeys the uncertainty principle. This is a statement that these terms are NOT well-defined beyond a certain realm. This is the definition of uncertainty I had walking into this discussion.

Do you view that the purely mathematical expression of the uncertainty principle from Fourier analysis is logically equivalent, no more no less, than the HUP? Do you agree that the Fourier analysis description of the uncertainty principle is about the inability to ascribe clear meaning to these variables? This is also nicely represented by Griffiths in his QM book, in a less mathematical way.

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