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.
Предметные области Scopus
- Статистическая и нелинейная физика
- Математическая физика