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## Homework Statement

I would appreciate feedback on the following two problems:

(1) For a given operator A with no explicit time dependence I am asked to show that d/dt(e

^{At})=A(e

^{At})

(2) A free wave packet of width Δx is traveling at a constant velocity v

_{0}=p

_{0}/m. I am asked to estimate the time-energy uncertainty relation.

## Homework Equations

## The Attempt at a Solution

(1) Is this as straightforward as it appears to be? Probably isn't, right? Is this to be solved using Ehrenfest's theorem? Or how?

(2) I can easily show that ΔEΔt ~ ħ but is this what I am plainly asked, or am I rather asked to arrive at a more exact result (i.e. find the proportionality coefficient)?