Symmetries of quantum graphs and the inverse scattering problem
(2005) In Advances in Applied Mathematics 35(1). p.5870 Abstract
 The Schrodinger equation on a graph together with a set of selfadjoint boundary conditions at the vertices determine a quantum graph. If the graph has one or more infinite edges one can associate a scattering matrix to the quantum graph. It is proved that if such a graph has internal symmetries then the boundary conditions, and hence the selfadjoint operator describing the quantum system, in general cannot be reconstructed from the scattering matrix. In addition it is shown that if the Schrodinger operator possesses internal symmetry then there exists a different quantum graph associated with the same scattering matrix.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/237635
 author
 Boman, J and Kurasov, Pavel ^{LU}
 organization
 publishing date
 2005
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 inverse scattering problem, quantum graph, schrodinger operator
 in
 Advances in Applied Mathematics
 volume
 35
 issue
 1
 pages
 58  70
 publisher
 Elsevier
 external identifiers

 wos:000229709500004
 scopus:19144361977
 ISSN
 10902074
 DOI
 10.1016/j.aam.2004.10.002
 language
 English
 LU publication?
 yes
 id
 a6c2ccbe57d642d68fe5734c6bed2251 (old id 237635)
 date added to LUP
 20160401 12:28:07
 date last changed
 20201208 03:44:53
@article{a6c2ccbe57d642d68fe5734c6bed2251, abstract = {The Schrodinger equation on a graph together with a set of selfadjoint boundary conditions at the vertices determine a quantum graph. If the graph has one or more infinite edges one can associate a scattering matrix to the quantum graph. It is proved that if such a graph has internal symmetries then the boundary conditions, and hence the selfadjoint operator describing the quantum system, in general cannot be reconstructed from the scattering matrix. In addition it is shown that if the Schrodinger operator possesses internal symmetry then there exists a different quantum graph associated with the same scattering matrix.}, author = {Boman, J and Kurasov, Pavel}, issn = {10902074}, language = {eng}, number = {1}, pages = {5870}, publisher = {Elsevier}, series = {Advances in Applied Mathematics}, title = {Symmetries of quantum graphs and the inverse scattering problem}, url = {http://dx.doi.org/10.1016/j.aam.2004.10.002}, doi = {10.1016/j.aam.2004.10.002}, volume = {35}, year = {2005}, }