2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57442We discuss a model of a leaky quantum wire and a family of quantum dots described by Laplacian in $L^2(\mathbb{R}^2)$ with an attractive singular perturbation supported by a line and a finite number of points. The discrete spectrum is shown to be nonempty, and furthermore, the resonance problem can be explicitly solved in this setting; by Birman-Schwinger method it is reformulated into a Friedrichs-type model.Latex2e, 10 pagesMathematical PhysicsMesoscale and Nanoscale PhysicsSpectral TheoryQuantum Physics81V99text