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

2024/11/18 by Marius Beceanu, Beceanu, Marius, H. Dharma Kwon +1
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2411.11787

openalex publication_date 2024/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we prove that Schrödinger's equation with a Hamiltonian of the form H=-Δ+i(A ∇ + ∇ 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 L¹ → L^∞ 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.

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