Weighted decay for magnetic Schroedinger equation

TL;DR

This paper establishes long-time decay estimates in weighted norms for solutions to the 3D magnetic Schrödinger equation, extending classical results to include magnetic potentials.

Contribution

It develops spectral theory techniques to handle magnetic potentials, extending decay results previously known only for non-magnetic Schrödinger equations.

Findings

Proves dispersive decay in weighted norms for magnetic Schrödinger solutions.

Extends spectral theory of Agmon, Jensen, and Kato to magnetic cases.

Achieves decay estimates similar to non-magnetic scenarios with magnetic potentials included.

Abstract

We obtain a dispersive long-time decay in weighted norms for solutions of 3D Schroedinger equation with generic magnetic and scalar potentials. The decay extends the results obtained by Jensen and Kato for the Schroedinger equation without magentic potentials. For the proof we develop the spectral theory of Agmon, Jensen and Kato, extending the high energy decay of the resolvent to the magnetic Schroedinger equation.