Dynamical versions of Morgan's Uncertainty Principle and Electromagnetic Schrödinger Evolutions

2025/02/04 by Shanlin Huang, Huang, Shanlin, Zhenqiang Wang +1
Physics and Astronomy · #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.2502.02255

openalex publication_date 2025/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper investigates the unique continuation properties of solutions of the electromagnetic Schrödinger equation i∂_tu(x,t)+(∇-i A)²u(x,t)=V(x,t)u(x,t) in ℝⁿ× [0,1], where A represents a time-independent magnetic vector potential and V is a bounded, complex valued time-dependent potential. Given 10 and there exists N_p>0 such that αβgt;N_p, then u≡ 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 Schrödinger equations.

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