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Step potential

  1. Nov 20, 2011 #1
    1. The problem statement, all variables and given/known data
    I'm working through a step potential and I am confused as to why one of the coefficients doesn't go to zero.

    V(x) = 0 when x < 0;
    V(x) = V_not when x > 0;

    a. Calculate reflection coefficient when E < V_not
    I can solve the reflection part, it is a step towards it that i am confused about.
    2. Relevant equations



    3. The attempt at a solution
    Now i know the solutions solve to:

    Aexp(ikx)+Bexp(-ikx) where k= sqrt(2mE)/hbar when x<0
    Cexp(lx) where l=sqrt(-2m(E-V_not)/hbar when x>0

    So my question is why doesn't B=0? Because when x->-infinity it goes to infinity so B has to be 0. The only reason i can think it wouldn't is because of tunneling. If this is the case how do I spot this. Is it only relevant in step potentials?
     
  2. jcsd
  3. Nov 20, 2011 #2

    vela

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    e-ikx is oscillatory. It doesn't blow up as x goes to -∞.
     
  4. Nov 20, 2011 #3
    Ah thank you. Now that brings up another question for the same problem but now E>Vo.

    The wave equations go to:
    Aexp(ikx) + Bexp(-ikx) when x < 0. k=sqrt(2mE)/hbar
    Cexp(ilx) + Dexp(-ilx) when x > 0. l=sqrt(2m(E-Vo))/hbar

    Now in this case why does D=0.
     
  5. Nov 20, 2011 #4

    vela

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    It's a boundary condition essentially. The idea here is you have an incident wave coming from the left. That corresponds to the A term. When it hits the potential step, you get a reflection, the B term, and a transmitted wave, the C term. The D term would correspond to a wave traveling to the right from x=+∞. You could certainly solve a problem with D not equal to 0, but it would be a different physical situation than the one you're interested in.
     
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