The Green function for simplest quantum graphs
K.K. SabirovPhysics Faculty, National University of Uzbekistan, Tashkent, UzbekistanU.A. AminovUrganch State University, Urganch, UzbekistanKh.Sh. SaparovUrganch State University, Urganch, UzbekistanM.K. KarimovUrganch State University, Urganch, UzbekistanKh. AbdikarimovUrganch State University, Urganch, Uzbekistan
ABI
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We treat the problem of the Green function for quantum graphs by focusing on such topologies as star and tree graphs. The exact Green function for the Schrdinger equation on primary star graphs is derived in the form of 3 3-matrix using the vertex boundary conditions providing continuity and current conservation. Extension of the approach for the derivation for the Green function on tree graph is presented. Possible practical applications of the obtained results are discussed.
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