00769nas a2200145 4500008004100000245003400041210003300075260001500108300001100123490000700134520040600141100002300547700001600570856003700586 2011 eng d00aLevinson's theorem for graphs0 aLevinsons theorem for graphs c2011/06/30 a0821020 v523 a 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).
1 aChilds, Andrew, M.1 aStrouse, DJ uhttp://arxiv.org/abs/1103.5077v2