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Hermitian symplectic geometry and extension theory

M. Harmer
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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 parameterisation of the Lagrange Grassmannian in terms of the unitary matrices $\U (n)$. This allows us to explicitly describe all self-adjoint boundary conditions for the Schroedinger operator on the graph in terms of a unitary matrix. We show that the asymptotics of the scattering matrix can be simply expressed in terms of this unitary matrix.

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M. Harmer. 2007-03-08. Hermitian symplectic geometry and extension theory. https://arxiv.org/abs/math-ph/0703027

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