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Our goal is to develop spectral and scattering theories for the one-dimensional Schrodinger operator with a long-range potential $q(x)$, $x\geq 0$. Traditionally, this problem is studied with a help of… Click to show full abstract
Our goal is to develop spectral and scattering theories for the one-dimensional Schrodinger operator with a long-range potential $q(x)$, $x\geq 0$. 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 $q' \in L^1$.
Keywords:
note schr;
long range;
range potential;
operator long
Journal Title: Letters in Mathematical Physics
Year Published: 2019
Link to full text (if available)
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Journal Title: Letters in Mathematical Physics
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!