Wave functions in the presence of a time-dependent field: Exact solutions and their application to tunneling

Abstract

Solutions to the time-dependent Schr\"odinger equation for a particle in a spatially uniform time-dependent field and some potentials of arbitrary form are proved to be like the time-independent eigenfunctions for an identical static potential. The field phase modulates the wave function and translates its envelope. This work applies directly to constant, linear, and parabolic static potentials and is self-consistent. Results for the modulation by a time-dependent field of the current through a rectangular barrier are relevant to the traversal time for tunneling and associated device limitations.