A regular analogue of the Smilansky model: spectral properties

Diana Barseghyan, Pavel Exner

We analyze spectral properties of the operator $H=\frac{{\partial }^2}{\partial x^2}-\frac{{\partial }^2}{\partial y^2}+{\omega }^2{y}^2-\lambda y^{2}V(xy)$ in $L^2({\mathbb{R}}^2)$, where $\omega \ne 0$ and $V…