Abstract
Here we give brief account of Hermitian symplectic spaces, showing that
they are intimately connected to symmetric as well as self-adjoint
extensions of a symmetric operator. Furthermore, we find an explicit
parametrization of the Lagrange Grassmannian in terms of the unitary
matrices
.
This allows us to explicitly describe all self-adjoint
boundary conditions for the Schrödinger operator on the graph in terms
of a unitary matrix. We show that the asymptotics of the scattering
matrix can be expressed simply in terms of this unitary matrix.