Find an explicit expression for the transmission of an Aharonov-Bohm ring that has arms of length $L_1$ and $L_2$, connected to two leads. The flux through the ring is $\Phi$. Assume junctions as described in the section 39.2 of the lecture notes with $u=0$. In order to solve use the method that is described in section 39.3 of the lecture notes.

Guidance: write a set of two coupled equations for the value $\psi_1$ and $psi_2$ of the wavefunction at the two junctions. Note that the two equations reflect the condition of having current conservation. Solve this set of equations assuming that an incident wave that has unit amplitude enters the first junction. The reflections and transmission amplitudes $r$ and $t$ can be expressed from $psi_1$ and $psi_2$ respectively.