Résonances multiples en limite semi-classique
In this note, we study the scattering amplitude for the Schrödinger equation with constant magnetic field. We consider the case where the strengh of the magnetic field goes to infinity and we discuss the competition between the magnetic and the electrostatic effects.
Strong asymptotic completeness is shown for a pair of Schrödinger type operators on a cylindrical Lipschitz domain. A key ingredient is a limiting absorption principle valid in a scale of weighted (local) Sobolev spaces with respect to the uniform topology. The results are based on a refined version of Mourre’s method within the context of pseudo-selfadjoint operators.