Mild singular potentials as effective Laplacians in narrow strips

Abstract

We propose to obtain information on one-dimensional Schrödinger operators on bounded intervals by approaching them as effective operators of the Laplacian in thin planar strips.  Here we develop this idea to get spectral knowledge of some mild singular potentials with Dirichlet boundary conditions.  Special preparations, including a result on perturbations of quadratic forms, are included as well.