One-dimensional Schrödinger operators with general point interactions. (English) Zbl 1289.47089

The authors consider various forms of boundary conditions for general one-dimensional Schrödinger operators with one or a finite number of point interactions including \(\delta\)- and \(\delta'\)-interactions, and the cases of a \(\delta'\)-potential and \(\delta\)-magnetic potential. For these operators, spectral properties are studied; the possibility of the norm resolvent approximation by operators with some types of \(\delta\)-potentials is investigated.


47E05 General theory of ordinary differential operators
47A55 Perturbation theory of linear operators
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis