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Inverse Problems for Quantum Graphs: Recent Developments and Perspectives

Kurasov, Pavel LU (2011) In Acta Physica Polonica. Series A: General Physics, Physics of Condensed Matter, Optics and Quantum Electronics, Atomic and Molecular Physics, Applied Physics 120(6A). p.132-141
Abstract
An introduction into the area of inverse problems for the Schrodinger operators on metric graphs is given. The case of metric finite trees is treated in detail with the focus on matching conditions. For graphs with loops we show that for almost all matching conditions the potential on the loop is not determined uniquely by the Titchmarsh-Weyl function. The class of all admissible potentials is characterized.
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author
organization
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type
Contribution to journal
publication status
published
subject
in
Acta Physica Polonica. Series A: General Physics, Physics of Condensed Matter, Optics and Quantum Electronics, Atomic and Molecular Physics, Applied Physics
volume
120
issue
6A
pages
132 - 141
publisher
Institute of Physics, Polish Academy of Sciences
external identifiers
  • wos:000301171100032
ISSN
0587-4246
language
English
LU publication?
yes
id
e4a77331-2e6a-4c62-bbba-8af268849cb1 (old id 2493662)
alternative location
http://przyrbwn.icm.edu.pl/APP/PDF/120/a120z6ap58.pdf
date added to LUP
2012-05-11 15:20:33
date last changed
2016-04-15 22:45:45
@article{e4a77331-2e6a-4c62-bbba-8af268849cb1,
  abstract     = {An introduction into the area of inverse problems for the Schrodinger operators on metric graphs is given. The case of metric finite trees is treated in detail with the focus on matching conditions. For graphs with loops we show that for almost all matching conditions the potential on the loop is not determined uniquely by the Titchmarsh-Weyl function. The class of all admissible potentials is characterized.},
  author       = {Kurasov, Pavel},
  issn         = {0587-4246},
  language     = {eng},
  number       = {6A},
  pages        = {132--141},
  publisher    = {Institute of Physics, Polish Academy of Sciences},
  series       = {Acta Physica Polonica. Series A: General Physics, Physics of Condensed Matter, Optics and Quantum Electronics, Atomic and Molecular Physics, Applied Physics},
  title        = {Inverse Problems for Quantum Graphs: Recent Developments and Perspectives},
  volume       = {120},
  year         = {2011},
}