Babak Etemadi

Fourier Series Representation of Low-Lying Eigenfunctions for a Particle on the Torus

A Fourier series method for finding the low-lying eigenfunctions and eigenvalues of the Schrödinger equation for a particle on the surface of a torus is given.

Surface distortion effects on quantum dot helium

The Schrodinger equation for a quantum mechanical particle constrained to a surface includes a potential term dependent on surface curvature. We use differential forms to derive this term and employ Monge representations for two surfaces to obtain specific expressions for the potential. We calculate the first order perturbative effect of this potential on the ground state energy of model quantum dot helium. We find that the energy shift can be sensitive to the detailed shape of the surface distortion. This dependence arises from the Coulomb repulsion between the electron pair, which causes each electron to preferentially sample (or not sample) regions where physical curvature leads to comparatively large values of the distortion potential.

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

Abstract 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.