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

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