Abstract:

We return to the Schroedinger operator H(x,y) = -\frac{\partial^2 \ }{\partial x^2} + \frac{1}{2} \left (-\frac{\partial^2 } {\partial y^2}+ y^2 \right )+\lambda y \delta(x)  x,y\in R^2 -- a paradigm model for multimode quantum graphs, and discuss it using a scattering approach, shedding some light on previous results, and study some related operators.