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→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.Comment: 4 pages, no fig