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arXiv · 2405.17715

Modified Jost solutions of Schr\"odinger operators with locally $H^{-1}$ potentials

Milivoje Lukić·Xingya Wang
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Abstract

We study Jost solutions of Schr\"odinger operators with potentials which decay with respect to a local $H^{-1}$ Sobolev norm; in particular, we generalize to this setting the results of Christ--Kiselev for potentials between the integrable and square-integrable rates of decay, proving existence of solutions with WKB asymptotic behavior on a large set of positive energies. This applies to new classes of potentials which are not locally integrable, or have better decay properties with respect to the $H^{-1}$ norm due to rapid oscillations.

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Milivoje Lukić, Xingya Wang. 2024-05-28. Modified Jost solutions of Schr\"odinger operators with locally $H^{-1}$ potentials. https://arxiv.org/abs/2405.17715

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