3 research outputs found

    Wave functions in the neighborhood of a toroidal surface; hard vs. soft constraint

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    The curvature potential arising from confining a particle initially in three-dimensional space onto a curved surface is normally derived in the hard constraint q0q \to 0 limit, with qq 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

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    The Schrodinger equation for an electron near an azimuthally symmetric curved surface Σ\Sigma in the presence of an arbitrary uniform magnetic field B\mathbf B is developed. A thin layer quantization procedure is implemented to bring the electron onto Σ\Sigma, leading to the well known geometric potential VCh2kV_C \propto h^2-k and a second potential that couples ANA_N, the component of A\mathbf A normal to Σ\Sigma to mean surface curvature, as well as a term dependent on the normal derivative of ANA_N evaluated on Σ\Sigma. 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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