Schrödinger operators in \(L^2(\mathbb{R})\) with pointwise localized potential (Q1300031)

The author constructs a lower semi-bounded, self-adjoint realization of the Schrödinger operator \(-\Delta+ \sum k_j\delta_{a_j}\) in \(L^2(\mathbb{R})\). The conditions on the sequences \((k_j)_{j\in\mathbb{Z}}\) and \((a_j)_{j\in\mathbb{Z}}\) are more general than those in the monograph [\textit{S. Albeverio}, \textit{F. Gesztesy}, \textit{R. Høegh-Krohn} and \textit{H. Holden}, ``Solvable models in quantum mechanics'', Springer, New-York, etc. (1988; Zbl 0679.46057)]. In particular, these conditions allow \(a_{j+1}- a_j\) to tend to zero. Moreover, the domain of self-adjointness, a subspace of \(H^1(\mathbb{R})\), is given explicitly.