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Quantum - Square barrier (help!)

  1. Oct 15, 2009 #1

    Determine the transmission coefficient for a rectangular barrier. Treat separately the three cases E<0, E=Vo, E>Vo (note that the wave function inside the barrier is different in the three cases.
    V(x) = Vo > 0 for -a < x < a
    = 0 for |x| > a

    I attempted to do this like the finite square well and do it per "zone", because I'm not sure how to go about dealing with the energy first.

    If I call - infinity -> -a "zone 1" and the potential there is zero, the general solution should be:
    [tex]\varphi[/tex] = A[tex]e^{-kx}[/tex] + B[tex]e^{kx}[/tex], but the first term blows up to -infinity, so we're left with
    [tex]\varphi[/tex] = B[tex]e^{kx}[/tex].

    Can someone tell me what is wrong with this logic?
    For E<Vo and x < -a [tex]\varphi[/tex] should include both A and B and be imaginary, but I don't know why.
  2. jcsd
  3. Oct 15, 2009 #2
    I'm sure it's apparent that this is from a textbook, (Griffiths 2.33) but it is study, not homework. Please don't disregard on that basis.
  4. Oct 15, 2009 #3
    To generalize a little bit more, this is is my basic question... why is the incoming wave to a square barrier complex?
  5. Oct 15, 2009 #4
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