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arXiv · 1203.6557

Levinson's theorem for graphs II

Andrew M. Childs·David Gosset
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Abstract

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.

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Andrew M. Childs, David Gosset. 2012-11-21. Levinson's theorem for graphs II. https://doi.org/10.1063/1.4757665

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