Fulop-Tsutsui interactions on quantum graphs

Understand

We examine scale invariant Fulop-Tsutsui couplings in a quantum vertex of a general degree $n$.

• We demonstrate that essentially same scattering amplitudes as for the free coupling can be achieved for two $(n-1)$-parameter Fulop-Tsutsui subfamilies if $n$ is odd, and for three $(n-1)$-parameter Fulop-Tsutsui subfamilies if $n$ is even.
• We also work up an approximation scheme for a general Fulop-Tsutsui vertex, using only $n$ $\delta$ function potentials.