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arXiv · 2502.02255

Dynamical versions of Morgan's Uncertainty Principle and Electromagnetic Schr\"{o}dinger Evolutions

Shanlin Huang·Zhenqiang Wang
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Abstract

This paper investigates the unique continuation properties of solutions of the electromagnetic Schr\"{o}dinger equation $$ i\partial_{t}u(x,t)+(\nabla-i A)^{2}u(x,t)=V(x,t)u(x,t)\,\,\,\, \mbox{in} \,\,\,\mathbb{R}^{n}\times [0,1], $$ where $A$ represents a time-independent magnetic vector potential and $V$ is a bounded, complex valued time-dependent potential. Given $1 0$ and there exists $N_{p}>0$ such that \begin{equation*} \alpha\beta>N_p, \end{equation*} then $u\equiv 0$. These results can be interpreted as dynamical versions of the uncertainty principle of Morgan's type. Furthermore, as an application, our results extend to a large class of semi-linear Schr\"{o}dinger equations.

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Shanlin Huang, Zhenqiang Wang. 2025-02-04. Dynamical versions of Morgan's Uncertainty Principle and Electromagnetic Schr\"{o}dinger Evolutions. https://arxiv.org/abs/2502.02255

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