najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2015-6-6-762-766najo-889Research ArticlePAPERS, PRESENTED AT THE CONFERENCEPAPERS, PRESENTED AT THE CONFERENCEThe Green function for simplest quantum graphsSabirovK. K.

Tashkent 

karimjonsabirov@yahoo.comAminovU. A.

Urganch

SaparovKh. Sh.

Urganch

KarimovM. K.

Urganch

AbdikarimovKh.

Urganch

Physics Faculty, National University of UzbekistanUzbekistanUrganch State UniversityUzbekistan20151508202566762766Copyright © Sabirov K.K., Aminov U.A., Saparov K.S., Karimov M.K., Abdikarimov K., 20252025Sabirov K.K., Aminov U.A., Saparov K.S., Karimov M.K., Abdikarimov K.Sabirov K.K., Aminov U.A., Saparov K.S., Karimov M.K., Abdikarimov K.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/889

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 Schr¨odinger 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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The authors declare that there are no conflicts of interest present.