Abstract: Quantum systems consisting of multiple manifolds with different dimesnionalities can be described using the von Neumann theory of self-adjoint extensions. The extensions can be characterized by their domains i.e. boundary conditions. In this talk, we will discuss a simple case of a free particle on a half-line connected to a half-space, spectral properties of the Hamiltonian and scattering on the connecting point. We then move on to describe a more complicated model of a ball with two half-lines connected to it, on which we study scattering and its resonances.