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Potential Step and Wave Functions

  1. Apr 5, 2015 #1
    1. The problem statement, all variables and given/known data


    Untitled.png

    2. Relevant equations


    3. The attempt at a solution

    For x>b, Ψ(x) = Ae-ikx + Beikx , where k = (√2mE)/hbar
    a<x<b Ψ(x) = Ce-ik'x + Deik'x , where k = (√2m(U2 - E)/hbar

    This is the problem part
    0<x<a Ψ(x) = Fsink''x , where k = (√2m(E+U1)/hbar
    I think this should be a standing wave, but am not sure if I am correct or not as I've never encountered a question like this before.

    x<0 Ψ(x) = 0
     
    Last edited: Apr 5, 2015
  2. jcsd
  3. Apr 5, 2015 #2
  4. Apr 5, 2015 #3
    I think you solution is correct. As concerns the standing wave, note that the spatial wave function should be multiplied by exp(-iwt) with w=E/hbar in order to get the solution to the Shrodinger equation. This will give you a standing wave.
     
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