Using uncertainty principle to estimate ground state energy

[whatupbaby]

Homework Statement

Use the uncertainty principle to estimate the ground state energy of a particle of mass "m" is moving in a linear potential given by

V(x) = ∞ for x≤ 0
V(x) = αx for x ≥ 0

Homework Equations

ΔxΔp ≥ [STRIKE]h[/STRIKE]/2

The Attempt at a Solution

I've looked at a similar problem with the harmonic oscillator potential which was a lot simpler because it is symmetric around x=0 making <x> = 0 and <p> = 0. I know an arbitrary energy level E will cut the potential at x=0 and x = E/α but I am unsure of how to proceed.

 

[vela]

Try drawing qualitatively what the ground state wave function will look like. The picture should give you an idea of the relevant wavelength and hence the momentum.