Bound States in Curved Quantum Layers
Mathematical Physics
2009-11-07 v1 Mesoscale and Nanoscale Physics
math.MP
Spectral Theory
Quantum Physics
Abstract
We consider a nonrelativistic quantum particle constrained to a curved layer of constant width built over a non-compact surface embedded in . We suppose that the latter is endowed with the geodesic polar coordinates and that the layer has the hard-wall boundary. Under the assumption that the surface curvatures vanish at infinity we find sufficient conditions which guarantee the existence of geometrically induced bound states.
Cite
@article{arxiv.math-ph/0102033,
title = {Bound States in Curved Quantum Layers},
author = {Pierre Duclos and Pavel Exner and David Krejcirik},
journal= {arXiv preprint arXiv:math-ph/0102033},
year = {2009}
}
Comments
20 pages in LaTeX