Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 53 1 2011 ASYMPTOTIC ANALYSIS FOR GREEN FUNCTIONS OF AHARONOV-BOHM HAMILTONIAN WITH APPLICATION TO RESONANCE WIDTHS IN MAGNETIC SCATTERING 1 37 EN Hideo Tamura 10.18926/mjou/41395 The Aharonov–Bohm Hamiltonian is the energy operator which governs quantum particles moving in a solenoidal field in two dimensions. We analyze asymptotic properties of its Green function with spectral parameters in the unphysical sheet. As an application, we discuss the lower bound on resonance widths for scattering by two magnetic fields with compact supports at large separation. The bound is evaluated in terms of backward scattering amplitudes by a single magnetic field. A special emphasis is placed on analyzing how a trajectory oscillating between two magnetic fields gives rise to resonances near the real axis, as the distance between two supports goes to infinity. We also refer to the relation to the semiclassical resonance theory for scattering by two solenoidal fields. No potential conflict of interest relevant to this article was reported.