Inverse Problems for Quantum Graphs: Recent Developments and Perspectives |

P. Kurasov
^{a,b,c}^{a}Dept. of Mathematics, LTH, Lund Univ., Box 118, 221 00 Lund, Sweden
^{b}Dept. of Mathematics, Stockholm Univ., 106 91, Stockholm, Sweden
^{c}Dept. of Physics, St. Petersburg Univ., 198904 St. Peterhof, Russia |

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An introduction into the area of inverse problems for the SchrÃ¶dinger 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. |

DOI: 10.12693/APhysPolA.120.A-132 PACS numbers: 03.65.Nk, 73.63.-b, 85.35.-p |