TY - JOUR
T1 - Levinson's theorem for graphs II
JF - Journal of Mathematical Physics
Y1 - 2012
A1 - Andrew M. Childs
A1 - David Gosset
AB - 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.
VL - 53
U4 - 102207
UR - http://arxiv.org/abs/1203.6557v2
CP - 10
J1 - J. Math. Phys.
U5 - 10.1063/1.4757665
ER -