SHADOW SCATTERING BY MAGNETIC-FIELDS IN 2 DIMENSIONS

We study the semi-classical asymptotic behavior of total scattering cross sections for Schrodinger operators with magnetic fields compactly supported. It is known that the quantum cross sections double the classical ones in the semi-classical limit for Schrodinger operators with finite-range potentials. This fact is called the shadow scattering in the potential scattering theory. We here prove that the shadow scattering is not in general expected for the magnetic scattering case.