Why multiple scattering in double wells is easy to solve

[aaaa202]

For a double well consider an incident wave from the left.
The wave gets transmitted and reflected at first well. The transmitted wave then hits the second well where it also gets both reflected and transmitted. The reflected part then hits the first well where it reflects and hits the second well and this process continues ad infinum. What I found was that it was not very hard to find the resulting amplitudes traveling in various directions if we just write up a system of equations and solve it (I think you have all seen how one applies periodic boundary conditions to the Schrödinger equation etc.) But why is it fundamentally so easy? I can't really see why it should physically be so easy since I have just accounted for how complicated the infinite process of reflections is. What is the miracle here?
I guess it is a stupid question since I should just accept the maths..

 

[Bill_K]

This is like the well-known anecdote about John von Neumann...

"What trick?" asked von Neumann; "all I did was sum the infinite series."

 

[aaaa202]

Thank you )