Minimal potential results for the Schrodinger equation in a slab
Analysis of PDEs
2013-09-03 v1
Abstract
Consider the Schrodinger equation -\Delta u =(k+V) u in an infinite slab S= \R^{n-1}x (0,1), where V is a bounded potential supported on a set D of finite measure. We prove necessary conditions for the existence of nontrivial admissible solutions. These conditions involve the sup. of |V|, the measure of D, and the distance of k from the "special set" {\pi^2 m^2, m positive integer}. In many cases, these inequalities are sharp.
Keywords
Cite
@article{arxiv.1309.0233,
title = {Minimal potential results for the Schrodinger equation in a slab},
author = {Laura De Carli and Steve Hudson and Xiaosheng Li},
journal= {arXiv preprint arXiv:1309.0233},
year = {2013}
}