Resonator with a Сorrugated Boundary: Numerical Results

— We consider a two-dimensional quantum system consisting of a resonator with the Neumann condition, to which N small similar resonators are attached along the boundary through small holes. The main purpose is to study the limiting case for . It is shown that in this limit the problem is reduced to a boundary value problem with an energy-dependent boundary condition of the Robin type. Asymptotic methods are used, as well as approximations of the eigenstates of the system obtained using the pinhole model. The results are compared with numerically obtained values.