English

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.

Keywords

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