336 research outputs found
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 parameters and bend location of the tube.Comment: 14 pages, 5 tables, 6 figure
Electron wave functions on in a static magnetic field of arbitrary direction
A basis set expansion is performed to find the eigenvalues and wave functions
for an electron on a toroidal surface subject to a constant magnetic
field in an arbitrary direction. The evolution of several low-lying states as a
function of field strength and field orientation is reported, and a procedure
to extend the results to include two-body Coulomb matrix elements on is
presented.Comment: 18 pages, 6 figure
Coupling curvature to a uniform magnetic field; an analytic and numerical study
The Schrodinger equation for an electron near an azimuthally symmetric curved
surface in the presence of an arbitrary uniform magnetic field
is developed. A thin layer quantization procedure is implemented to
bring the electron onto , leading to the well known geometric potential
and a second potential that couples , the component of
normal to to mean surface curvature, as well as a term
dependent on the normal derivative of
evaluated on . Numerical results in the form of ground state
energies as a function of the applied field in several orientations are
presented for a toroidal model.Comment: 12 pages, 3 figure
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