Find the most general $S$ matrix that represents a 3 channel junction under the assumptions that the channel wavefunctions have to match at the node of the junction.

Remarks: The unitarity of the S matrix implies that the sum of the probability currents that flow out of the junction is zero (Kirchhoff law). We have here a generalization of the 2 channel delta function: hence the solution should depend in a free parameter $u$ that describes the potential energy of the junction. For some more tips see section 39.2 of the lecture notes.