2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115003We consider a periodic strip in the plane and the associated quantum waveguide with Dirichlet boundary conditions. We analyse finite segments of the waveguide consisting of $L$ periodicity cells, equipped with periodic boundary conditions at the ``new'' boundaries. Our main result is that the distance between the first and second eigenvalue of such a finite segment behaves like $L^{-2}$.3 pagesMathematical PhysicsSpectral Theorytext