Transmission Coefficient of a double delta function potential

jmm5872

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:

ψ_I = Ae^ikx+Be^-ikx for (x < -L)
ψ_II = Ce^ikx+De^-ikx for (-L < x < L)
ψ_III = Ee^ikx+Fe^-ikx for (L < x )

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

turin

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.