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Schrödinger for a Step

  1. Mar 14, 2012 #1
    1. The problem statement, all variables and given/known data

    Proton travelling along the x-axis approaches a potential barrier at x = 0

    Height of potential barrier - U0 = 20eV
    Proton Velocity = 44km/s = 44,000m/s

    Asked to show that the solution to the one dimensional time independent Schrödinger equation is
    [itex]\psi[/itex](x) = A sin (kx - ϕ)

    2. Relevant equations

    I know that when the potential is constant and
    V(x) = V0 < E

    That the solution is the one given, but only because I have read it, I'm not sure how to get get there myself.


    3. The attempt at a solution

    Reading about it, what I can get is maybe you treat it as one end of an infinite well, so at the step/wall the wave function has to = 0.
    Then the need for it to be zero at the walls and non zero away from the wall requires the addition of half a period.
    Hence the phi.
    But other than that I don't really get it, could anyone help?

    Cheers
     
  2. jcsd
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