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The relativistic inverse scattering problem for quantum graphs

K.K. SabirovNational University of Uzbekistan, 4 University St., 100074, Tashkent, UzbekistanZ. A. SobirovNational University of Uzbekistan, 4 University St., 100074, Tashkent, UzbekistanО. В. КарповаNational University of Uzbekistan, 4 University St., 100074, Tashkent, UzbekistanA. A. SaidovTurin Polytechnic University in Tashkent, 17 Niyazov St., 100095, Tashkent, Uzbekistan
Nanosystems Physics Chemistry Mathematicsjournal2015en
ABI

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.

Topics

Spectral Theory in Mathematical PhysicsQuantum chaos and dynamical systemsQuantum Mechanics and Non-Hermitian Physics

Identifiers

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

Citations and references

Cited by 08 references
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