5 research outputs found
Wave functions in the neighborhood of a toroidal surface; hard vs. soft constraint
The curvature potential arising from confining a particle initially in
three-dimensional space onto a curved surface is normally derived in the hard
constraint limit, with the degree of freedom normal to the
surface. In this work the hard constraint is relaxed, and eigenvalues and wave
functions are numerically determined for a particle confined to a thin layer in
the neighborhood of a toroidal surface. The hard constraint and finite layer
(or soft constraint) quantities are comparable, but both differ markedly from
those of the corresponding two dimensional system, indicating that the
curvature potential continues to influence the dynamics when the particle is
confined to a finite layer. This effect is potentially of consequence to the
modelling of curved nanostructures.Comment: 4 pages, no fig
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
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