Two-parametric ${\delta }^{\prime }$-interactions: approximation by Schrödinger operators with localized rank-two perturbations

Abstract

We construct a norm resolvent approximation to the family of point interactions $f(+0)=\alpha f(-0)+\beta f^{\prime }(-0)$, $f^{\prime }(+0)={\alpha }^{-1}{f}^{\prime }(-0)$ by Schrödinger operators with localized rank-two perturbations coupled with short range potentials. In particular, a new approximation to the ${\delta }^{\prime }$-interactions is obtained.

Submitted to JPA. 13 pages, 1 figure

References in corpus (2)

• Controlling a resonant transmission across the ${\delta }^{\prime }$-potential: the inverse problem
• On S-matrix of Schrodinger Operators with Non-Symmetric Zero-Range Potentials

Cited by in corpus (8)

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• The semi-classical limit with a delta-prime potential
• Conditions for realizing one-point interactions from a multi-layer structure model