Decay estimates for Schrödinger's equation with magnetic potentials in three dimensions

Fuente: arXiv
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Main Authors: Beceanu, Marius, Kwon, Hyun-Kyoung
Format: Preprint
Published: 2024
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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
id 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