Eigenstates of Möbius nanostructures including curvature effects

M\"obius-shell structures and their physical properties have recently received considerable attention experimentally and theoretically. In this work, eigenstates and associated eigenenergies are determined for a quantum-mechanical particle bounded to a M\"obius shell including curvature contributions to the kinetic-energy operator. This is done using a parametrization of the M\"obius shell--found by minimizing the elastic energy of the full structure--and employing differential-geometry methods. It is shown that inclusion of curvature contributions to the kinetic energy leads to splitting of the otherwise doubly degenerate groundstate and significantly alters the form of the groundstate and excited-state wavefunctions. Hence, we anticipate qualitative changes in the physical properties of M\"obius-shell structures due to surface confinement and curvature effects.