An approximation to ${\delta }^{\prime }$ couplings on graphs

Abstract

We discuss a general parametrization for vertices of quantum graphs and show, in particular, how the ${\delta }_s^{\prime }$ and ${\delta }^{\prime }$ coupling at an $n$ edge vertex can be approximated by means of $n+1$ couplings of the $\delta$ type provided the latter are properly scaled.

10 pages, LaTeX, 1 figure added, to be published in J. of Phys. A