Singular Schrödinger operators as limits of point interaction Hamiltonians
The results of this paper concern the approximation of Schrödinger operators of the form \(H=-\Delta+\mu\) in one and three space dimensions, where \(\mu\) is a finite Radon measure. In dimension one, \(H\) is shown to be the norm resolvent limit of \(-\Delta+\mu_n\) if \(\mu_n\) is a sequence of finite Radon measures weakly converging to \(\mu\). In particular \(H\) may be approximated by operators with smooth potentials as well as by operators with point interactions. In three dimensions a result concerning the approximation with point interactions, similar to the one above, is proved for \(\mu\) belonging to a large but restricted class of finite Radon measures. Applications to concrete examples are given.
scientific article; zbMATH DE number 1160071