  For perturbed Stark operators $Hu=-u^{\prime\prime}-xu+qu$, the author has
proved that $\limsup_{x\to \infty}{x}^{\frac{1}{2}}|q(x)|$ 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.
