127 research outputs found
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
Curvature induced toroidal bound states
Curvature induced bound state (E < 0) eigenvalues and eigenfunctions for a
particle constrained to move on the surface of a torus are calculated. A limit
on the number of bound states a torus with minor radius a and major radius R
can support is obtained. A condition for mapping constrained particle wave
functions on the torus into free particle wave functions is established.Comment: 6 pages, no figures, Late
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