Our goal is to develop spectral and scattering theories for the one-dimensional Schrödinger operator with a long-range potential q(x), x≥ 0. Traditionally, this problem is studied with a help of the Green–Liouville approximation. This requires conditions on the first two derivatives q ^′(x) and q ^{′ ′}(x). We suggest a new Ansatz that allows us to develop a consistent theory under the only assumption q ^′∈ L ¹.