Potential approximations to $δ'$: an inverse Klauder phenomenon with norm-resolvent convergence

Details Potential approximations to $δ'$: an inverse Klauder phenomenon with norm-resolvent convergence Potential approximations to $δ'$: an inverse Klauder phenomenon with norm-resolvent convergence

2001-03-22

arxiv.org/abs/math-ph/0103027v2

Commun. Math. Phys. 224 (2001), 593-612

Physics

Mathematical Physics

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

Scientific paper

10.1007/s002200100567

We show that there is a family Schroedinger operators with scaled potentials
which approximates the $\delta'$-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.

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