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Transmission Coefficient of a double delta function potential

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Mar6-12, 09:36 PM
P: 43
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?
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Mar9-12, 10:38 PM
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turin's Avatar
P: 2,327
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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