Asymptotics in all regimes for the Schrödinger equation with time-independent coefficients
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913060076126208 |
|---|---|
| author | Looi, Shi-Zhuo Sussman, Ethan |
| author_facet | Looi, Shi-Zhuo Sussman, Ethan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20991 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotics in all regimes for the Schrödinger equation with time-independent coefficients Looi, Shi-Zhuo Sussman, Ethan Analysis of PDEs Primary 35C20, Secondary 58J50, 35K15, 35Q40 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. |
| title | Asymptotics in all regimes for the Schrödinger equation with time-independent coefficients |
| topic | Analysis of PDEs Primary 35C20, Secondary 58J50, 35K15, 35Q40 |
| url | https://arxiv.org/abs/2407.20991 |