Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.26144 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908916845117440 |
|---|---|
| author | Song, Yilin Wang, Ying Zheng, Jiqiang Zhou, Ruihan |
| author_facet | Song, Yilin Wang, Ying Zheng, Jiqiang Zhou, Ruihan |
| contents | In this paper, we establish a Paley-Wiener type uncertainty principle for Schrödinger equations with bounded electric and magnetic potentials,
\begin{align*}
i\partial_tu+Δ_Au+V(t,x)u=0,\,\,u(0,x)=u_0(x),
\end{align*}
where $Δ_A=(\nabla-iA)^2$ denotes the magnetic Schrödinger operator.
Specifically, under suitable assumptions on $A$ and $V$, we show that if a solution
$u$
exhibits linear exponential decay and support property in one spatial direction at times $t=0$ and $t=1$ respectively, then
$u$ must vanish identically. This result extends the theorem of Kenig-Ponce-Vega [Ann. Sci. Éc. Norm. Supér. (4) 47 (2014), 539-557] to the case $A\neq0$.
We overcome the difficulty brought by the magnetic potential which breaks the translation invariance in the leading term of Hamiltonian $H=Δ_A+V$. As a direct consequence, we also obtain a uniqueness result for a class of semi-linear Schrödinger equation with electromagnetic potentials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_26144 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Paley-Wiener type uniqueness result for the electromagnetic Schrödinger equation Song, Yilin Wang, Ying Zheng, Jiqiang Zhou, Ruihan Analysis of PDEs 35Q55 In this paper, we establish a Paley-Wiener type uncertainty principle for Schrödinger equations with bounded electric and magnetic potentials, \begin{align*} i\partial_tu+Δ_Au+V(t,x)u=0,\,\,u(0,x)=u_0(x), \end{align*} where $Δ_A=(\nabla-iA)^2$ denotes the magnetic Schrödinger operator. Specifically, under suitable assumptions on $A$ and $V$, we show that if a solution $u$ exhibits linear exponential decay and support property in one spatial direction at times $t=0$ and $t=1$ respectively, then $u$ must vanish identically. This result extends the theorem of Kenig-Ponce-Vega [Ann. Sci. Éc. Norm. Supér. (4) 47 (2014), 539-557] to the case $A\neq0$. We overcome the difficulty brought by the magnetic potential which breaks the translation invariance in the leading term of Hamiltonian $H=Δ_A+V$. As a direct consequence, we also obtain a uniqueness result for a class of semi-linear Schrödinger equation with electromagnetic potentials. |
| title | A Paley-Wiener type uniqueness result for the electromagnetic Schrödinger equation |
| topic | Analysis of PDEs 35Q55 |
| url | https://arxiv.org/abs/2603.26144 |