Sharp bounds for finitely many embedded eigenvalues of perturbed Stark type operators
Institutional Repository Document
Overview
Research
Identity
Other
View All
Overview
abstract
For perturbed Stark operators $Hu=-u^{primeprime}-xu+qu$, the author has proved that $limsup_{x o infty}{x}^{frac{1}{2}}|q(x)|$ must be larger than $frac{1}{sqrt{2}}N^{frac{1}{2}}$ in order to create $N$ linearly independent eigensolutions in $L^2(mathbb{R}^+)$. In this paper, we apply generalized Wigner-von Neumann type functions to construct embedded eigenvalues for a class of Schr"odinger operators, including a proof that the bound $frac{1}{sqrt{2}}N^{frac{1}{2}}$ is sharp.
