TY - JOUR
T1 - Levinson's theorem for graphs
JF - Journal of Mathematical Physics
Y1 - 2011
A1 - Andrew M. Childs
A1 - DJ Strouse
AB - We prove an analog of Levinson's theorem for scattering on a weighted (m+1)-vertex graph with a semi-infinite path attached to one of its vertices. In particular, we show that the number of bound states in such a scattering problem is equal to m minus half the winding number of the phase of the reflection coefficient (where each so-called half-bound state is counted as half a bound state).
VL - 52
U4 - 082102
UR - http://arxiv.org/abs/1103.5077v2
CP - 8
J1 - J. Math. Phys.
U5 - 10.1063/1.3622608
ER -