Abstract
In this paper, we give an Avron–Herbst type formula for the propagator generated by the free Hamiltonian with crossed constant magnetic and time-dependent electric fields. As an application of the formula, we give a result of the existence of the wave operators under some appropriate conditions on the time-dependent electric field and the potential. Finally, in the case where the electric field is time-independent, we consider the problem of the asymptotic completeness of the wave operators.
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