How Long Does a Quantum Particle or Wave Stay in a Given Region of Space?

Abstract

The delay time associated with a scattering process is one of the most important dynamical aspects in quantum mechanics. A common measure of this is the Wigner delay time based on the group velocity description of a wave packet, which may easily indicate superluminal or even negative times of interaction that are unacceptable. Many other measures such as dwell times have been proposed, but also suffer from serious deficiencies, particularly for evanescent waves. One important way of realising timescales that are causally connected to the spatial region of interest relies on utilising the dynamical evolution of extra degrees of freedom, called quantum clocks, such as the precession of the spin of an electron in an applied magnetic field or the coherent decay or growth of light in an absorptive or amplifying medium placed within the region of interest. Here we provide a review the several approaches developed to answer the basic question “how much time does a quantum particle (or wave) spend in a specified region of space?” While a unique answer still evades us, important progress has been made in understanding the timescales and obtaining positive definite times of interaction by noting that all such clocks are affected by spurious scattering concomitant with the very clock potentials, however, weak they be, and by eliminating the spurious scattering.