Some properties of one-dimensional point interactions

Abstract

In this review paper we shall give a brief account of some properties of so called point interactions that describe a potentials spatially localized. A different families of one-dimensional point interactions are investigated and then relevant tunneling times are calculated. Than we demonstrate how a bound state in the continuum may be generated applying supersymmetric quantum mechanics. Finally, it is shown how the latter method may be used to tailor phase rigidity of one-dimensional point interactions.