ON THE EMBEDDED EIGENVALUES AND DENSE POINT SPECTRUM OF THE STARK-LIKE HAMILTONIANS

The point spectrum lying on the essential spectrum is investigated for the one-dimen dimensional Schrodinger operator -d2/dx2+q(x) with deca ying potential q, and weakly perturbed Stark-like operator -d2/dx2 -/x /(alpha)sign x+q(x). An elementary constructive technique is developed to obtain various results concerning embedded eigenvalues of Schrodin ger operators. In Section 3 a constructive example of the Stark-like o perator with the potential q decaying slightly slowlier than O(1/x/(1- alpha/2)) and dense point spectrum on the whole real axis is presented .