Remarks on the Avron-Herbst Type Formula for N-body Quantum Systems in Constant Electric and Magnetic Fields

Abstract

In this paper, for N ≥ 2, we give a natural derivation of the Avron-Herbst type formula for the time evolution generated by an N -body Hamiltonian with constant electric and magnetic fields. By virtue of the formula, some scattering problems can be reduced to those in the case where the constant electric and magnetic fields are parallel to each other. As an application of the formula, we give the result of the asymptotic completeness for the systems which have the only charged particle and some neutral ones in crossed constant electric and magnetic fields.