MATHEMATICA BOHEMICA, Vol. 139, No. 2, pp. 259-267, 2014

Quantum-graph vertex couplings: some old and new approximations

Stepan Manko

Stepan Manko, Department of Physics, Faculty of Nuclear Science and Physical Engineering, Czech Technical University in Prague, Pohraniční 1288/1, 405 01 Děčín, Czech Republic, e-mail:

Abstract: In 1986 P. Šeba in the classic paper considered one-dimensional pseudo-Hamiltonians containing the first derivative of the Dirac delta function. Although the paper contained some inaccuracy, it was one of the starting points in approximating one-dimension self-adjoint couplings. In the present paper we develop the above results to the case of quantum systems with complex geometry.

Keywords: quantum graph; vertex coupling; singularly scaled potential

Classification (MSC 2010): 81Q35, 34L40

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