Transmission Coefficient of a double delta function potential

  1. V(x) = |g| (δ(x+L)+δ(x-L)

    Consider scattering from a repulsive twin-delta function potential.

    Calculate R and T.

    I'm mostly confused about computing the T coefficients for multiple barriers. Would I compute the T coefficient for the barrier at x = -L and at x = L seperately? Then, instead of having to take an integral for the total T, for a large forbidden region, I can simply multiply the two T coefficients together since the Δx is essentially zero for a delta well.

    Also, for the wavefunction in each region I have:

    ψI = Aeikx+Be-ikx for (x < -L)
    ψII = Ceikx+De-ikx for (-L < x < L)
    ψIII = Eeikx+Fe-ikx for (L < x )

    But the incident wave is from left to right so F = 0. Am I on the right track?
  2. jcsd
  3. turin

    turin 2,326
    Homework Helper

    I think that you are on the right track.

    Probably you only have one T; only for x > L, and then you don't actually match the I,R part to the T part, but rather match the I,R part to the left side of the intermediate part, and then match the right side of the intermediate part to the T part.
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