The Schrödinger operator on graphs and topology

Details The Schrödinger operator on graphs and topology The Schrödinger operator on graphs and topology

2000-04-12

arxiv.org/abs/math-ph/0004015v1

Russian Math Surveys, 52 (1997) n 6 pp 1320-1321

Physics

Mathematical Physics

LATEX2e, 3 pages

Scientific paper

Symplectic vector-valued scalar product is constructed on the spaces of solutions of the real discrete Shrodinger equation with fixed value of the spectral parameter on graphs. It takes values in the first homology group of the graph. This scalar product plays fundamental role in the Scattering theory for the graphs with tails. In particular, all unitarity properties of scattering follow from elementary symplectic geometry

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