On the Green function for a particle in a uniform electric field

Abstract

A closed form is presented for the one-dimensional Green function of a particle in a uniform electric field pervading all space. The Green function is found to be analytic in the whole complex energy plane; some interesting implications of this analyticity are discussed. Further analysis employing more realistic boundary conditions at infinity indicates, however, that no physical system (no matter how large) is adequately represented by the uniform field model for arbitrarily weak field intensities, though the limitation is of no practical importance.