Equivalence of Local and Separable Realizations of Discontinuity-Inducing Contact Interaction

Abstract

We consider the regularized approximations of the discontinuity-inducing singular zero-range interaction in one-dimensional quantum mechanics. We prove that two known approximations, one in terms of local potential and the other in terms of separable function are equivalent. We further show that the interaction allows the perturbative treatment through the coupling constant renormalization.