@article {1228,
title = {Levinson{\textquoteright}s theorem for graphs II},
journal = {Journal of Mathematical Physics},
volume = {53},
year = {2012},
month = {2012/11/21},
pages = {102207},
abstract = { We prove Levinson{\textquoteright}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.
},
doi = {10.1063/1.4757665},
url = {http://arxiv.org/abs/1203.6557v2},
author = {Andrew M. Childs and David Gosset}
}