P Kurasov and F Stenberg 2002 J. Phys. A: Math. Gen. 35 101 doi:10.1088/0305-4470/35/1/309
P Kurasov1 and F Stenberg
Show affiliationsThe inverse scattering problem on branching graphs is studied. The definition of the Schrödinger operator on such graphs is discussed. The operator is defined with real potentials with finite first momentum and using special boundary conditions connecting values of the functions at the vertices. It is shown that in general the scattering matrix does not determine the topology of the graph, the potentials on the edges and the boundary conditions uniquely.
03.65.Ge Solutions of wave equations: bound states
05C25 Graphs and groups (See also 20F65)
81U40 Inverse scattering problems
34L40 Particular operators (Dirac, one-dimensional Schrödinger, etc.)
Issue 1 (11 January 2002)
Received 30 March 2001, in final form 29 October 2001
Published 21 December 2001
P Kurasov and F Stenberg 2002 J. Phys. A: Math. Gen. 35 101
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