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Using uncertainty principle to estimate ground state energy

  1. Oct 6, 2011 #1
    1. The problem statement, all variables and given/known data
    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

    2. Relevant equations
    ΔxΔp ≥ [STRIKE]h[/STRIKE]/2


    3. 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.
     
  2. jcsd
  3. Oct 7, 2011 #2

    vela

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    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.
     
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