Sharp bounds for finitely many embedded eigenvalues of perturbed Stark type operators

摘要

For perturbed Stark operators Hu = -u '' - xu + qu, the author has proved that lim sup(x ->infinity) x(1/2) vertical bar q(x)vertical bar must be larger than 1/root 2N(1/2) in order to create N linearly v2 independent eigensolutions in L-2 (R+) [29]. In this paper, we apply generalized Wigner-von Neumann type functions to construct embedded eigenvalues for a class of Schrodinger operators, including a proof that the bound 1/root 2N(1/2) is sharp.