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

Authors
Type
Preprint
Publication Date
Sep 21, 2004
Submission Date
Sep 21, 2004
Identifiers
DOI: 10.1238/Physica.Regular.072a00013
arXiv ID: quant-ph/0409141
Source
arXiv
The curvature potential arising from confining a particle initially in three-dimensional space onto a curved surface is normally derived in the hard constraint $q \to 0$ limit, with $q$ 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.