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I am reading this note on potential scattering by Siu-Hung Tang and Maciej Zworski. Just wondering if there is a scattering theory for the Schrödinger with a non-decaying potential $- \Delta + V$ on the real line, like, for some $V$ that has an non-zero asymptote as $|x| \rightarrow \infty$.

Any reference/comment would be great - Thanks in advance!

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  • $\begingroup$ A lot of what they did in those notes (the ODE and Wronskian analysis etc) can be reproduced when the potential has non-zero asymptotes. The specific case where $V$ is the step-function is also well-studied (e.g. en.wikipedia.org/wiki/…). $\endgroup$
    – Willie Wong
    Commented May 11, 2022 at 16:43
  • $\begingroup$ @WillieWong Thanks! I'll check it out $\endgroup$
    – alby
    Commented May 12, 2022 at 15:39

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