Abstract
Our goal is to develop spectral and scattering theories for the one-dimensional Schrodinger operator with a long-range potential q(x), $$x\ge 0$$. 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 $$q' \in L^1$$.
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