Semiclassical resolvent estimates for the magnetic Schrödinger operator

Abstract We obtain semiclassical resolvent estimates for the Schrödinger operator in , , where is a semiclassical parameter, and are real‐valued electric and magnetic potentials independent of . If , , satisfy , , , , for , we prove that the norm of the weighted resolvent is bounded by , . We get better resolvent bounds for electric potentials which are Hölder with respect to the radial variable and magnetic potentials which are Hölder with respect to the space variable. For long‐range electric potentials which are Lipschitz with respect to the radial variable and long‐range magnetic potentials which are Lipschitz with respect to the space variable we obtain a resolvent bound of the form , .