Decay estimates for Schrödinger's equation with magnetic potentials in three dimensions
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916670578098176 |
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| author | Beceanu, Marius Kwon, Hyun-Kyoung |
| author_facet | Beceanu, Marius Kwon, Hyun-Kyoung |
| contents | In this paper we prove that Schrödinger's equation with a Hamiltonian of the form $H=-Δ+i(A \nabla + \nabla A) + V$, which includes a magnetic potential $A$, has the same dispersive and solution decay properties as the free Schrödinger equation. In particular, we prove $L^1 \to L^\infty$ decay and some related estimates for the wave equation.
The potentials $A$ and $V$ are short-range and $A$ has four derivatives, but they can be arbitrarily large. All results hold in three space dimensions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_11787 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Decay estimates for Schrödinger's equation with magnetic potentials in three dimensions Beceanu, Marius Kwon, Hyun-Kyoung Analysis of PDEs Mathematical Physics In this paper we prove that Schrödinger's equation with a Hamiltonian of the form $H=-Δ+i(A \nabla + \nabla A) + V$, which includes a magnetic potential $A$, has the same dispersive and solution decay properties as the free Schrödinger equation. In particular, we prove $L^1 \to L^\infty$ decay and some related estimates for the wave equation. The potentials $A$ and $V$ are short-range and $A$ has four derivatives, but they can be arbitrarily large. All results hold in three space dimensions. |
| title | Decay estimates for Schrödinger's equation with magnetic potentials in three dimensions |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2411.11787 |