Summary: [For part I see the authors, ibid. 52, No. 8, 082102, 9 p. (2011; Zbl 1272.81081)] 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 \(n = 1\).{
©2012 American Institute of Physics}