Asymptotics in all regimes for the Schrödinger equation with time-independent coefficients

2024/07/30 by Shi-Zhuo Looi, Looi, Shi-Zhuo, Ethan Sussman +1
Mathematics · #35K15 #35Q40 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary 35C20 #Secondary 58J50 #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2407.20991

openalex publication_date 2024/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using the recent analysis of the output of the low-energy resolvent of Schrödinger 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 Schrödinger 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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