Kiselev A., Remling C., Simon B. Effective Perturbation Methods for One-Dimensional Schrodinger Operators (47K, LaTeX) ABSTRACT. We introduce a general Prufer type transformation for discrete and continuous one-dimensional Schrodinger operators. This transformation relates the solutions of -y''+(V_0+V)y=Ey to a reference solution of the unperturbed equation -y''+V_0 y=Ey. We use these transforms to study embedded eigenvalues and perturbations of absolutely continuous spectra by potentials of Pearson type.