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## Homework Statement

We have to estimate the ground state energy of an infinite potential well (1d) using an argument based on the heisenberg uncertainty principal. We then are supposed to compare it with the exact value from the eigenvalue equation.

## Homework Equations

Below

## The Attempt at a Solution

I am not really sure where to start on this one but this is what I tried:

ΔxΔp = h and since there is no potential where the particle is all the energy is kinetic so classically Ke = E = p^2/2m. then to look at change i just did

Δp = [itex]\sqrt{ΔE2m}[/itex]

and subbed it into the above unvertainty principle. This gives

Δx[itex]\sqrt{ΔE2m}[/itex] = h

[itex]Δx^{2}[/itex]ΔE2m = [itex]h^{2}[/itex]

ΔE = [itex]\frac{h^{2}}{2mΔx^2}[/itex]

The problem is that even if this is somewhat right I am not sure what I really did. Can anyone give me some hints?