Levinson's theorem for graphs

Details Levinson's theorem for graphs Levinson's theorem for graphs

2011-03-25

arxiv.org/abs/1103.5077v2

Journal of Mathematical Physics 52, 082102 (2011)

Physics

Mathematical Physics

10 pages, 1 figure; v2: minor corrections

Scientific paper

10.1063/1.3622608

We prove an analog of Levinson's theorem for scattering on a weighted (m+1)-vertex graph with a semi-infinite path attached to one of its vertices. In particular, we show that the number of bound states in such a scattering problem is equal to m minus half the winding number of the phase of the reflection coefficient (where each so-called half-bound state is counted as half a bound state).

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