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Time-energy uncertainty and derivative of an operator
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[QUOTE="jfizzix, post: 4963388, member: 190322"] I'm guessing that there is a standard formula for a free wave packet of given [itex]\Delta x[/itex] and [itex]p_{0}[/itex], to which the problem is referring. Failing that, the best I can think of is to find a limit to the momentum uncertainty with [itex]\Delta p\geq \frac{\hbar}{2 \Delta x}[/itex]. Then, knowing [itex]p_{0}[/itex] and a bound for [itex]\Delta p[/itex], you can use that [itex]E=\frac{p^{2}}{2m}[/itex] and the propagation of uncertainty [itex](\Delta E)^{2}\approx (\frac{\partial E}{\partial p})^{2}(\Delta p)^{2}[/itex] Getting an estimate for the time uncertainty is a bit trickier (since time is not an observable), but you can say that [itex]\Delta t = \frac{\Delta x}{(\frac{d <x>}{dt})}[/itex] That's about all I can say on the matter, though. [/QUOTE]
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Introductory Physics Homework Help
Time-energy uncertainty and derivative of an operator
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