Asymptotics in all regimes for the Schr\"odinger equation with time-independent coefficients

Shi-Zhuo Looi; Ethan Sussman

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arXiv · 2407.20991

Asymptotics in all regimes for the Schr\"odinger equation with time-independent coefficients

Shi-Zhuo Looi·Ethan Sussman

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Abstract

Using the recent analysis of the output of the low-energy resolvent of Schr\"odinger operators on asymptotically conic manifolds (including Euclidean space) when the potential is short-range, we produce detailed asymptotic expansions for the solutions of the initial-value problem for the Schr\"odinger equation (assuming Schwartz initial data). Asymptotics are calculated in all joint large-radii large-time regimes, these corresponding to the boundary hypersurfaces of a particular compactification of spacetime.

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Shi-Zhuo Looi, Ethan Sussman. 2024-07-30. Asymptotics in all regimes for the Schr\"odinger equation with time-independent coefficients. https://arxiv.org/abs/2407.20991

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