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I was studying the scatter states of a particle in a double delta potential given in this link:

Double delta function well – scattering states

But I dont understand how equations (20) and (21) were obtained, any one of the equation is sufficient actually, the other can be obtained.

Any help appreciated!

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    $\begingroup$ Comment to the question (v2): It would be good if OP (or somebody else?) could try to make the question formulation self-contained, so one doesn't have to open the link to understand the question. $\endgroup$
    – Qmechanic ♦
    Commented Oct 17, 2015 at 11:06
  • $\begingroup$ Courage, your link is now dead, providing a good example of another reason why we insist on the site for the questions to be self-contained. I found this pdf, but I'm not sure whether the equation numbering corresponds to your original source - could you please check that update the question? $\endgroup$
    – stafusa
    Commented Mar 22, 2021 at 17:40

1 Answer 1

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The solution considers waves propagating in the positive $x$ direction, since for $x>a$ the wave function is $\psi(x) = F e^{ikx}$. Accordingly, the internal transmission rate for the internal segment $-a \le x \le a$ is given by the relative amplitude of the $e^{ikx}$ component, the one "transmitted" in the same direction as the outgoing wave. Similarly, the reflection coefficient is given by the "reflected" $e^{-ikx}$ component propagating in the opposite direction. Since in the inner region $\psi(x) = C e^{ikx} + D e^{-ikx}$, where both $C$ and $D$ are proportional to $A$, this gives $T_i = |C|^2/|A|^2$ and $R_i = |D|^2/|A|^2$, with $C$ and $D$ as in Eqs.(11), (12).

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