K. K. Sabirov, Z. A. Sobirov, O. V. Karpova, A. A. Saidov, “The relativistic inverse scattering problem for quantum graphs”, Nanosystems: Physics, Chemistry, Mathematics, 2015, Volume 6, Issue 2,Pages <nobr>192

The relativistic inverse scattering problem for quantum graphs

K. K. Sabirov^a, Z. A. Sobirov^a, O. V. Karpova^ab, A. A. Saidov^b

^a National University of Uzbekistan, 4 University St., 100074, Tashkent, Uzbekistan
^b Turin Polytechnic University in Tashkent, 17 Niyazov St., 100095, Tashkent, Uzbekistan

Abstract: 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

Received: 02.02.2015

Language: English

DOI: 10.17586/2220-8054-2015-6-2-192-197