A numerical study of the spectrum and eigenfunctions on a tubular arc

The Hamiltonian for a particle constrained to move on the surface of a curved nanotube is derived using the methods of differential forms. A two-dimensional Gram–Schmidt orthonormalization procedure is employed to calculate basis functions for determining the eigenvalues and eigenstates of a tubular arc (a nanotube in the shape of a hyperbolic cosine) with several hundred scattering centers. The curvature of the tube is shown to induce bound states that are dependent on the curvature parameter and bend location of the tube.