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(eAt)=A(eAt)
(2) A free wave packet of width Δx is traveling at a constant velocity v0=p0/m. I am asked to estimate the time-energy uncertainty relation.
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)?