According to my book, uncertainty Q = 0 (where Q is an observable) is true when the state function is an eigenfunction.(adsbygoogle = window.adsbygoogle || []).push({});

The energy eigenfunction for a particle in a 1-D box with infinitely high walls is sin(n*pi*x/a). This implies that the linear momentum, p, is known with zero uncertainty. By the uncertainty principle, the position, x, should have infinite uncertainty. This should mean an eigenfunction whose absolute value squared is a constant.

But the eigenfunction above (sin[]) doesn't meet that requirement.

I'd really appreciate it if someone could help me out here Thanks!

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# Eigenfunction & Uncertainty

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