%0 Journal Article
%J Journal of Mathematical Physics
%D 2012
%T Levinson's theorem for graphs II
%A Andrew M. Childs
%A David Gosset
%X We prove Levinson's theorem for scattering on an (m+n)-vertex graph with n semi-infinite paths each attached to a different vertex, generalizing a previous result for the case n=1. This theorem counts the number of bound states in terms of the winding of the determinant of the S-matrix. We also provide a proof that the bound states and incoming scattering states of the Hamiltonian together form a complete basis for the Hilbert space, generalizing another result for the case n=1.
%B Journal of Mathematical Physics
%V 53
%P 102207
%8 2012/11/21
%G eng
%U http://arxiv.org/abs/1203.6557v2
%N 10
%! J. Math. Phys.
%R 10.1063/1.4757665