Given the uncertainty in momentum, calculate the uncertainty in Energy

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Homework Statement



I am given that E = (hbar)^2 k^2 / 2m. I am suppose to calculate the uncertainty in energy(ΔE).

I am also given the wave equation.

I am given Δp (uncertainty in p), Ko (wave number). and that Δp << hbar Ko.

Homework Equations



I believe the equation is ΔE = sqrt(<E^2> - <E>^2).

The Attempt at a Solution



So I found <E> = <p^2> / 2m. How am I suppose to find <E^2>? I tried to just square the given E formula and then find <E^2> that way. However, I get <hbar^4 k^4 > / 4m^2. I do not know what to do from there.

Any help would be great. Thanks!
 

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