Dispersive decay for the magnetic Schrödinger equation

We obtain a dispersive long-time decay in weighted norms for solutions of 3D Schrödinger equation with generic magnetic and scalar potentials. The decay extends the results obtained by Jensen and Kato for the Schrödinger equation without magnetic 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 Schrödinger equation. Our methods allows us extend the result to all dimension n⩾3.