Dwell times for light and electrons

Abstract

Using a time-dependent scattering theory for light the authors obtain expressions for the time that light spends in a finite dielectric medium surrounded by vacuum, the so-called dwell time. Given an incoming wavepacket, they focus upon the light scattered in an arbitrary direction. In view of the similarity between Maxwell's equations and the Schrodinger equation, some useful results are derived for the case of Schrodinger potential scattering as well. They show that the dwell time of a Schrodinger particle is a derivative of the phase shifts with respect to the potential, rather than to energy as is the case for the phase-delay time. They indicate the relation to absorption arguments. Because the potential for classical waves is energy dependent, derivatives of the phase shift with respect to potential enter into the phase-delay time for classical waves.