SEMICLASSICAL RESOLVENT ESTIMATES FOR THE MAGNETIC SCHR ÖDINGER OPERATOR
Résumé
We obtain semiclassical resolvent estimates for the Schrödinger operator
(ih∇ + b)^2 + V in R^d , d ≥ 3, where h is a semiclassical parameter, V and b are real-valued electric and magnetic potentials independent of h.
Under quite general assumptions, we prove that the norm of the weighted resolvent is bounded by exp(Ch^{-2} log(h^{ -1} )) . 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 exp(Ch^{-1}) .
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