Displaying similar documents to “A duality between Schrödinger operators on graphs and certain Jacobi matrices”

Essential self-adjointness for combinatorial Schrödinger operators III- Magnetic fields

Yves Colin de Verdière, Nabila Torki-Hamza, Françoise Truc (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

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We define the magnetic Schrödinger operator on an infinite graph by the data of a magnetic field, some weights on vertices and some weights on edges. We discuss essential self-adjointness of this operator for graphs of bounded degree. The main result is a discrete version of a result of two authors of the present paper.

Quantum-graph vertex couplings: some old and new approximations

Stepan Manko (2014)

Mathematica Bohemica

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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.