%0 Journal Article
%J Journal of Mathematical Physics
%D 2011
%T Levinson's theorem for graphs
%A Andrew M. Childs
%A DJ Strouse
%X 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).
%B Journal of Mathematical Physics
%V 52
%P 082102
%8 2011/06/30
%G eng
%U http://arxiv.org/abs/1103.5077v2
%N 8
%! J. Math. Phys.
%R 10.1063/1.3622608