Spectral analysis of quantum nanoribbons

The aim of this thesis is the generalization of several theorems about the spectral behaviour of the Laplace?Beltrami operator with Dirichlet boundary condition on quantum nanoribbons to arbitrary dimension as well as finding the spectrum of the (curved) Möbius strip. The notion of a quantum ribbon in an arbitrary dimension is introduced along with the proper definition of a quantum Hamiltonian for such strip. Theorems about the localization of essential spectrum for asymptotically flat strips, about bound states in purely bent strips and Hardy inequalities for twisted strips are presented. The spectrum of the Möbius strip is tackled in three different models both analytically and numerically, with comparisons of the results. We prove the norm?resolvent convergence in the thin strip limit for two of those models.