NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2015, 6 (2), P. 192–197
The relativistic inverse scattering problem for quantum graphs
K. K. Sabirov – National University of Uzbekistan, Uzbekistan; karimjonsabirov@yahoo.com
Z. A. Sobirov – National University of Uzbekistan, Uzbekistan
O. V. Karpova – National University of Uzbekistan; Turin Polytechnic University in Tashkent, Uzbekistan
A. A. Saidov – Turin Polytechnic University in Tashkent, Uzbekistan
In this paper, we treat the inverse scattering problem for the Dirac equation on metric graphs. Using the known scattering data, we recover the potential in the Dirac equation. The Gel’fand-Levitan-Marchenko integral equation is derived and potential is explicitly obtained for the case of a primary star graph.
Keywords: quantum graph, inverse scattering problem, Dirac equation.
PACS 02.30.Zz, 03.65.Pm
DOI 10.17586/2220-8054-2015-6-2-192-197