Potential approximations to ${\delta }^{\prime }$: an inverse Klauder phenomenon with norm-resolvent convergence

Abstract

We show that there is a family Schroedinger operators with scaled potentials which approximates the ${\delta }^{\prime }$-interaction Hamiltonian in the norm-resolvent sense. This approximation, based on a formal scheme proposed by Cheon and Shigehara, has nontrivial convergence properties which are in several respects opposite to those of the Klauder phenomenon.

LaTeX2e, a revised version to be published in Commun. Math. Phys

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