Quantum-graph vertex couplings: some old and new approximations. (English) Zbl 1340.81014

Manko, Stepan

Math. Bohem. 139, No. 2, 259-267 (2014).

Summary: In 1986 P. Šeba in the classic paper [Rep. Math. Phys. 24, No. 1, 111–120 (1986; Zbl 0638.70016)] 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.

MSC:

81Q35	Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices
34L40	Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)

Keywords:

quantum graph; vertex coupling; singularly scaled potential

Citations:

Zbl 0638.70016