Existence of Bound States for Layers Built Over Hypersurfaces of Euclidean Space
Differential Geometry
2007-07-18 v6 Mathematical Physics
math.MP
Abstract
In this paper, we study the bound states of quantum layers. We prove that for the quantum layer built over a parabolic manifold which is not totally geodesic, if the second fundamantal form decays sufficiently fast, then the bound states exist. In the 2d case, we prove that the quantum layer over a convex surface whose second fundamental form tends to zero at infinity must have bound states.
Cite
@article{arxiv.math/0402252,
title = {Existence of Bound States for Layers Built Over Hypersurfaces of Euclidean Space},
author = {Christopher Lin and Zhiqin Lu},
journal= {arXiv preprint arXiv:math/0402252},
year = {2007}
}
Comments
19 pages