# Transmission Coefficient of a double delta function potential

• jmm5872
In summary, the conversation discusses scattering from a repulsive twin-delta function potential and the calculation of R and T coefficients for multiple barriers. The speaker is confused about computing the T coefficients separately for each barrier and whether the wavefunction should be matched to the T part or the intermediate part. The expert suggests that there is only one T coefficient for x > L and the wavefunction should be matched to the left side of the intermediate part.
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:

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?

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.

## 1. What is the definition of a double delta function potential?

A double delta function potential is a type of potential energy function that is commonly used in quantum mechanics to model two very narrow and closely spaced potential wells or barriers. It is represented mathematically as the sum of two delta functions, which are mathematical functions that are zero everywhere except at a single point.

## 2. How is the transmission coefficient of a double delta function potential calculated?

The transmission coefficient of a double delta function potential is calculated using the Schrödinger equation, which describes the behavior of quantum particles. The transmission coefficient is the ratio of the transmitted wave function to the incident wave function, and it can be calculated by solving the Schrödinger equation for the wave function at both sides of the potential barrier.

## 3. What is the physical significance of the transmission coefficient of a double delta function potential?

The transmission coefficient of a double delta function potential represents the probability that a quantum particle will pass through the potential barrier. It is a measure of the transmission efficiency of the barrier, with a higher transmission coefficient indicating a higher probability of transmission.

## 4. How does the width and height of the potential barrier affect the transmission coefficient?

The width and height of the potential barrier have a direct impact on the transmission coefficient of a double delta function potential. A wider and taller barrier will result in a lower transmission coefficient, meaning that there is a lower probability of the particle passing through the barrier. Conversely, a narrower and shorter barrier will have a higher transmission coefficient and a higher probability of transmission.

## 5. Can the transmission coefficient of a double delta function potential be experimentally measured?

Yes, the transmission coefficient of a double delta function potential can be experimentally measured by studying the behavior of quantum particles as they interact with the potential barrier. This can be done using techniques such as electron tunneling or particle scattering experiments. However, due to the nature of quantum mechanics, the exact value of the transmission coefficient may not always be measurable, but rather a statistical average of many measurements.

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